I meant to post half a hundred years ago but it's taken me a month of concerted effort to make it to page 1272, so ...
Somebody way back in the wild blue yonder posed a question as to Solas's MBTI type and I've spent way too much time mulling over it since then. So, a month too late, here's my suggestion for consideration.
I've seen him typed variously as INTJ, INTP, and INFJ. I'm going to (lengthily) support INTP.
So, for quick overview, here are the type functions of the these three proposed types:
INTJ: Ni/Te/Fi/Se (dominant perceiver)
INTP: Ti/Ne/Si/Fe (dominant judger)
INFJ: Ni/Fe/Ti/Se (dominant perceiver)
TMI re: functions: The J/P was not something used by Jung and was added by Meyers-Briggs. Being a J doesn't mean one is Judgy McJudgerson, just that one's dominant extroverted function prefers closure to possibilities. It refers to the first extroverted function in a stacking (not the first function!) and is therefore a little skewed when dealing with introverts. For example, an ENTJ is a dominant 'judger' because their lead extroverted function (also their first function, as is the case with all extroverts) is Te, which is a judging function (it prefers closure). In the case of an INTP, the P refers to their first extroverted function (Ne), which is a perceiving function (it prefers possibilities); however, they are dominant judgers because their leading function, Ti, is a judging function that prefers closure.
TMI: re: TMI: As their name suggests, extroverted functions are essentially the 'face' one shows to the world while introverted functions are the stuff that's happening internally. That's why introverts are introverts. Their primary stuff is going on in their heads and is not being directly shown to the outside world.
So much for the boring, convoluted stuff. Now Solas!
Solas and Ti
What is Ti?
Briefly, it's logical analysis and reasoning that delights in breaking things down to their essentials. It delights in careful speech, selecting words for maximum effectiveness in conveying meaning. It looks for inconsistencies and focuses on creating elegant systems. When there are problems, it examines them from multiple angles and finds solutions that maintain the essence of the system. When paired with Se, the result could be thought of as a skilled architect able to build elegant palaces or engineer a plan to keep the Tower of Pisa from collapsing. When paired with Ne, it creates an architect of ideas.
And this, I think, is Solas at his core. An architect of ideas.
* Solas is extremely particular about his words. And I mean beyond poetical eloquence. Consider the case of Solas 'lying' to Lavellan, betraying or otherwise hoodwinking her. I'd suggest that to Ti he did not do these things. He was very careful not to, sometimes putting more meaning in what was not said than what was. He uses words to wiggle out of situations that would either require complete truth (which he's not in a good position to offer) or an outright lie (which I don't think he wants to do, cf. his respect for Cassandra's straightforwardness).
Blackwall: It's a simple yes or no question!
Solas: Nothing about the fade is simple, especially not that.
Blackwall: Aha! So you do have experience in these matters!
Solas: I did not say that.
Cassandra: You must not have been far away.
Solas: I was not. I had come to hear of the Conclave, but I did not want to get close.
Cole: You're different, Solas. Sharper. You're in both places.
Solas: I visit the Fade regularly. Perhaps you are sensing traces of it.
In none of these examples (among many) is he lying. He's choosing his words very carefully so that he can mean what he says. Or say things without definitively saying something. Like with Blackwall, he doesn't say it isn't true, either, he just sidesteps the question. He tells Cassandra the truth, but does volunteer any further information or give away his true purpose. Hear what of the Conclave, Solas, dear? Likewise with Cole, he's telling the truth but not volunteering any further information. He comes close to a lie in the 'sensing traces' bit; surely Solas knows exactly why he feels that way to Cole, and it isn't likely Fade residue. But maybe there's a 5% possibility that that's the case, so he couches it in a 'perhaps' and thus is technically telling the truth. Note that this isn't the same as being completely open/volunteering information, but I think part of Solas's unhappiness lies in his perceived inability to do that in his current situation.
So, to Ti there is a world of difference between saying "I visit the Fade regularly. You are sensing traces of it." and "I visit the Fade regularly. Perhaps you are sensing traces of it." In other words, I don't think Solas cynically chose that phrasing to allow himself an out later on: "Ah, but I didn't lie!". Rather, he sees them as two completely different things, one true and the other not true. Let's artificially limit him to three options: 1) You are sensing traces of it. 2) Perhaps you are sensing traces of it. 3) I'm one of the Elvhen gods, so I feel weird. Of these, I suspect Solas's first inclination would be option 3, but for obvious reasons he can't say it. He then chooses option 2, because it is true, and rejects option 1 because it is false. I suppose this is why I find accusing Solas of lying to Lavellan a little harsh. He wasn't, technically. And to Ti, that 'technically' is of huge importance.
*Ti breaking things (especially ideas) down into their constituent parts or their foundations. Creating 'theories' that underpin everything. Contrast this to Te, the thinking function of the INTJ. Te likes plans, it organizes ideas and the physical world, it loves efficiency.
Cassandra: You also heard the voices at the Temple - is it so surprising that I listened to them?
Solas: Sadly, yes. Too few invested with authority posses the courage to alter their course.
Solas: They fear the appearance of weakness.
Solas has created an internal theory of power and authority that he reveals on occasion. Here is part of it. He abstracts; he is not talking about Cassandra's reactions, but of the reactions, methods, and reasoning of all persons in authority. Ti, as a judging function, has created its theory (that persons in authority will not alter course for fear of appearing weak), checks what he is observing against that theory and is surprised that the two don't line up. Solas is drawing a judgement against his ideal of authority and finding observed reality wanting; thus, he notes "sadly" that Cassandra is an exception to the rule.
Solas: The Wardens see themselves as the World's defense against the Blight, do they not?
Blackwall: Yes ... why do you sound so skeptical? Doesn't everyone know this?
Solas: When an Archdemon rises, they slay it. What will they do when all the Archdemons are slain?
Blackwall: Uh ... retire?
Solas: Without Archdemons there can be no Blights, is that the reasoning?
Blackwall: Right. Where are you going with this?
Solas: Nowhere. I hope they are correct.
Solas takes the concept of the Grey Wardens and breaks it down until he finds its fundamental tenent. He even says he's going "nowhere" with the idea, whereas results-oriented Te generally doesn't bother with trains to nowhere. Also note his bit of word trickery (again): "I hope they are correct." True, he probably hopes so. He doesn't say he thinks it likely, however. Or (as may be the case) that it will result in Epic Disaster Time. But he hopes it won't!
Iron Bull: [After saying that Thedas would be better off under the Qun] But the war to make that happen? That'd be ugly. A lot of good people would die.
Iron Bull: So I'm not hoping it happens. There! You happy?
Solas: Happy? No, quite the opposite.
Iron Bull: Oh, come on. I said I didn't want us to invade you!
Solas: No. You said this world would be brighter if all thinking individuals were stripped of individuality.
Solas: You only lack the will to get more blood on your hands.
Solas cuts IB's argument down to its ultimate point, and one that IB doesn't refute. I'd also suggest that this bit of dialogue is one of the stronger pieces of evidence for not having a feeling function high on Solas's list. Solas gives IB's emotion-based hope little weighting, and even flips it on him. He's not pleased that IB gives a crap about the people who would die. I would argue that, in an abstract way, Solas doesn't give a great deal of craps about the people who would die. Solas is more interested in ideological purity, in this case that of individual freedom. I think Solas's thinking lies along these lines: If IB's ideal of the Qun is correct but the means of achieving the ideal is not something IB can accept, then IB needs to reconsider his ideal. His phrasing is troubling, though. It suggests that Bull's lack of will to kill to achieve the ideal is a problem to Solas's mind. Perhaps meaning that Solas would be quite willing to wander into mass murder territory to achieve his ideal state of freedom (and the irony of that is delicious). Not that he wouldn't feel bad, but according to Solas in this dialogue, if I'm reading it right, his feeling bad about it is ultimately irrelevant and shouldn't stop him.
Solas: It is easier for people to believe they were tricked into making terrible decisions.
Solas: Competition brings passion, Cole, and passion lets people attach import to trivial things.
Solas: Even the lowliest peasant may find freedom in the safety of her thoughts.
Solas: ... Freedom is preferable to mindless obedience ...
Some of Solas's ideology coming out. Notice how it is abstract and generalized, observations being winnowed down to their core.
There are a lot more examples of what I perceive to be Solas's Ti coming out to play. Way too many. In general, I would suggest looking at Solas's first inclination in most dialogues. Is he first inclined to get along (Fe), to question ideas (Ti), to create/evaluate solutions (Te), to predict future outcomes (Ni), to consider possibilities (Ne), or to consider morality/personal reasoning (Fi)? I'd suggest that he, more often than not, prods people into considering and questioning IDEAS and the stances drawn from them. INTJs and INFJs lead with Ni, the great foreseer of outcomes. We very rarely see Solas do this. In fact, the two concrete examples of Solas attempting it have ended in disaster (locking the gods away or whatever it was he did, and planning on having Cory unlock the orb).
I have seen it suggested that Solas either sucks at what he claims to do or has really bad luck. I think it's more along the lines of Solas being driven by a Ti with its ideals pushed too far to seek to do something that is not in his sphere of competence at all. Namely, to act. Solas is a thinker not a doer. Solas suddenly had to create a plan and execute it (Te), and to foresee the implications and likely results (Ni). If Solas is an INTP it makes Te/Ni his shadow functions. I've heard them called the 'child functions' because, while we have access to them, we are not adept at using them and the results can be heavy handed and awkward. Which, I think, explains the results of Solas's attempts at world alteration. They weren't the results of a particularly hapless INTJ, though they can look like it because Solas was using INTJ functions to accomplish them. Instead, they were the hapless, semi-competent results of a brilliant, passionate philosopher forcing himself into the role of cunning, decisive mastermind.
Regarding his other functions, I'm comfortable with Ne, which would be the source of Solas's relative open-mindedness, his abstractness, his love of possibilities, and his craptacular track-record with decision-making. On Si, I think there's a general consensus that Sera's comment: "His mind is up a thousand years ago" aptly describes Solas. That is Si, considering, contemplating, even being stuck in the past. If he were INTJ or INFJ he would be focused on the future and not looking into the past (Si is not either of their function stacks). He wouldn't be forever comparing the present to the past, but he does, because Si. INTJs use Fi as their fourth function, which Solas could have, though none of the rest of the INTJs functions fit him very well, in my opinion.
As for INFJ, their second function is Fe while for INTPs it is their fourth function. Generally, the fourth function is weak and often unreliable due to being the function we develop latest in life. We use it all through our lives, but it takes time to become competent with it. Fe is the main social function, allowing one to get along in groups, act in socially appropriate ways, etc. (A very general description; Fi and Fe can be two of the hardest functions to distinguish). Now, we know Solas is one smooth operator. We know he can manipulate the social play of Orlesian politics to his benefit, and that he enjoys doing so. This certainly sounds like Fe as a dominant function. However, Solas is thousands of years old, with more than enough time to highly develop one's lowest function. I think the more definitive thing is when Solas uses Fe, not how. Check his dialogue with the other companions, especially Cassandra, IB, and Sera. He starts off engaging them with Ti/Ne (his natural preference), but eventually his Fe picks up on their discomfort/whatever and he uses it to soften the blow/end the conversation. He does this pretty frequently with Lavellan, too. So, yes, he is skilled at using Fe, arguably as skilled as an INFJ when he chooses to use it. But he doesn't use it automatically, by default, or as a first choice, suggesting to me that it isn't his dominant mode of expressing himself.