What Flemeth did in DA2 to come back to life is actually nothing like what Corypheus or the Archedemons do. Flemeth gave Hawke an amulet, said amulet was placed upon an altar of Mythal in a ritual conducted by an elf (Merrill), and her Flemeth body, not just Mythal spirit, materialized (either teleportation or rebirth, depending on Warden choice in Origins). What she did is actually more akin to random things done in the setting where we do some ritual and summon a demon. There was no body that suddenly transformed into Flemythal, as would be the case of Cory or the Archedemon.
Solas says the Evanuris were just mages. Well, they were more powerful than any mage we have seen in the post-Veil world, so that is obviously about as true as comparing an Archedemon to a Dragon, they have similarities, but they aren't the same. Solas himself, and Abelas, do not believe modern Elves to be Elves, and this has something to do with something more than their immortality and magical capabilities. The question then becomes, what were the Elvhen? Because they clearly aren't Elves (as we know them, humans with pointy ears and slight builds), and they clearly don't exist with the Veil up except in rare circumstances.
So, Solas says the Evanuris are powerful, Elvhen, mages. So, Mythal's power comes from 1) whatever the hell the Elvhen were (and by that I mean, their connection to the Fade, which remains ambiguous) 2) really old (related to being powerful) 3) magical (which is like saying water is wet).
But that's really all we have to go on. Solas answered about as many questions as if when you asked, "why is the sky blue?" and they said, "because."