Okay, I have a few hours of testing done. Apologies in advance for the long post to follow.
I decided to test out whether resting at camp was necessary, or if mounting and dismounting from the horse was sufficient.
First, I returned to Skyhold from the Exalted Plains (where I had been testing yesterday) and then I traveled to the Storm Coast, an area I had mostly cleared. I did the mount/dismount routine, without resting. My party consisted of Blackwall, Iron Bull, and Vivienne. This is the sequence of events there:
1. At 24 minutes, Iron Bull and Blackwall bantered.
2. At 26 minutes, Iron Bull and Vivienne bantered.
3. At 28 minutes, Iron Bull and Vivienne bantered.
4. At 35 minutes, Vivienne and Blackwall bantered.
5. At 36 minutes, Vivenne and Iron Bull bantered.
6. At 38 minutes, Iron Bull and Blackwall bantered.
7. At 41 minutes, Vivienne and Blackwall bantered.
8. At 42 minutes, Vivenne and Iron Bull bantered.
9. Found a codex quoting from a book called "Qun, Gurns, and Steel," heh.
10. At 44 minutes, Blackwall and Iron Bull bantered.
11. Ended it at the hour mark.
Summary: Nine banters! That's an unprecedented amount of banter for me. It was very shocking, especially because this was a group of members who had been mute with each other before this. Vivienne and Blackwall had never talked, Iron Bull and Vivienne had bantered once, and Iron Bull and Blackwall might have talked once before. Also, I wasn't idling most of the time; I was actively finishing up a quest. However, I did notice what appeared to be some kind of post-battle dialogue lag. Blackwall asked if everyone was all right, which I'm assuming is one of those things he says after an encounter is over... but it had been over for a few minutes already when he spoke up. This happened twice.
Second, I went to Val Royeaux. I wanted to see if the possible workaround might continue after moving to a different zone. I changed my party to Sera, Vivienne, and Cassandra, since I hadn't heard much banter between them. I ran around for a bit. Walked past the bard, and noticed that despite the subtitles being on, I didn't hear her singing. Came by later and it returned, however. Then I left the game idling in the background. I did not hear any banter for the hour I let them stand there. Additionally, I also do not seem to have music playing in the city; I have the background chatter people have described, but I didn't realize there was anything more.
Third, I exited Val Royeuax and journeyed to the Hinterlands with the same party. I did the mount/dismount routine (again, without resting) and then went about finding shards and completing a couple sidequests. This is what happened in the Hinterlands:
1. At 20 minutes, Sera and Vivienne bantered. Second time they've ever talked with each other in my game.
2. At 27 minutes, Sera and Vivienne bantered.
3. At 35 minutes, I noticed that I couldn't hear a scout's voice, even though I saw the subtitles.
4. At 1 hour and 9 minutes, Vivienne and Sera bantered again.
5. At 1 hour and 10 minutes, Sera and Cassandra bantered again.
6. At 1 hour and 26 minutes, Vivienne and Cassandra bantered (which was a first for me).
7. At 1 hour and 47 minutes, Vivienne and Cassandra bantered again.
8. I stopped at 1 hour and 50 minutes.
Summary: Six banters! Again, between characters that hadn't bantered much before. I also noticed that maybe (I dunno, obviously, considering my playthrough's general banter scarcity) these were early game banters? I'm in what I would consider Act 2 (after a certain change of scenery, as it were). Vivienne was discussing the Divine and the conclave and how surprised she was that the Inquisition was so organized by Cassandra. This might imply that banters aren't triggering, rather than being silently going on in the background.
Anyway, as a last mini-test, I mounted and dismounted in the Hinterlands, and then traveled to Val Royeaux to see if any banter would trigger now. Waited twenty minutes, nothing.
As far as combat dialogue, I didn't realize there was any aside from "[low health character] needs help!" or the victory cries they have (usually noticeable after they crush a nug into the ground because I sent a stray bolt of magic...). Is there an example of what it's supposed to sound like?