Mystery and Night - The last two Old Gods, the last remaining sealed Evanuris.

I like thinking about evanuris/spirit match ups but given what Solas himself tells about demons being spirits with a corrupted purpose I like to think about both their original "pure" purpose and their corrupted "demon" version.

So Solas, whose name means pride (and dear lord is he with his 'i get to change the nature of the whole world without consulting anyone... Twice' bullshit) but who seems to prefer to dispense wisdom and approves of those who seek it, obviously seems like a wisdom spirit > pride demon just like his friend in his companion quest.

And the Elven ruins both at her temple and in the crossroads pretty thoroughly depict Mythal as a goddess of justice/vengeance. This combined with her desire for vengeance against the others makes me put her in the Justice spirit > Vengeance demon category, like Justice in dao:a/da2.

So if Fen'harel = Wisdom > Pride
and Mythal = Justice > vengeance
Then for the remaining Evanuris I'd guess:
Dirthamon = Knowledge > Fear
Sylaise = Love > Envy
Andruil = Perseverance > Hunger
Ghilan'nain = Curiosity > Obsession
Elgar'nan = Valour > Rage
Falon'din = Command > Oppression
June = Creativity? > Sloth?

Obviously I agree with you about Dirthamin god of secrets being Fear, and I think his uncorrupted self is knowledge. What is secrecy if not knowledge concealed? What does secrecy create if not the Fear of discovery and the Fear of what others are hiding? Just look at how terrified/paranoid his followers were in the temple of Dirthamin during their last days.

But for Sylaise Envy was my first thought because of that whole 'everything they can do, she can do better' inscription in the temple of Mythal which absolutely stinks of jealousy: dragonage.fandom.com/wiki/Codex_entry:_Song_to_Sylaise
But we don't know what envy demons are a corruption of: Admiration? Compassion? Love? If one of the latter two then that would give the dalish perception of her as a goddess of healing and childbirth a source.

For Andruil goddess of the hunt whose followers prayed not to be the hunted - a hunter who over hunts, who hunts people instead of animals, who'll hunt no matter what even in the dangers of the void. She evokes hunger demons the most to me. The insatiable consumers. The guys who make cannibals, vampires, and werewolves. Like the one who possessed a starving man in Tevinter Nights and twisted his need into an insatiable greedy hunger. I've thought about, and dismissed, various potential purposes that hunger could be a corruption of. Not Moderation, Satiation, or Generosity, demons don't seem to be complete opposites of their spirit versions per se. And Need isn't really a purpose/virture/concept so much as it's just a fact, so it doesn't feel quite right either. And i thought of a Survival spirit giving people what they need without giving them unending hunger like the demon does... But it looks a bit out of place with the other spirit purposes. Then i was like oh what people struggling to survive are exhibiting - what the subsistence farmer and the fisherman entirely reliant on the catch is showing - is a type of Perseverance. A spirit we already know exists from the Next One short story.
Alternately we may be looking at Sacrifice not as another word for her demonic form sacrificing Elven lives to her glory or entertainment - but instead in it's positive form, a parent going hungry to feed their child, sacrificing your own dreams or life to help another, a hunter who thanks every animal they kill for their sacrifice and is sure not to waste a single piece.

Ghilan'nain's mural, probable trespasser notes about her experiments, and her lab in Tevinter Nights, all paint a picture of the mad scientist to me. Someone whose so obsessed with their work that the human cost does not matter. Uncorrupted this may be simple curiosity, or perhaps Purpose since I think Solas makes the connection between a spirit of purpose and a demon of desire, and Obsession might just be a type of Desire demon.

I'm inclined to agree that Elgar'nan does come off as more raging/anger/smashy smashy then he does an actual spirit/demon of vengeance. But then I had to think about what his spirit purpose would be, the only example we have is Audric who is curiosity/anger but
a ) he's a complex spirit/greater dead who has all his human memories, so not a normal spirit. On the otherhand maybe what he is is closer to what the evanuris is then a normal spirit? And
b ) nothing about Elgar'nan has screamed curiosity to me, it would be a fascinating development if it did turn out to be so, but so far got nothing to support it.
What we do know about him is that he was the leader, and that he was a general in one or more great wars for the Elven people. Now that works just as well for Command as it does for Valour. And the leader of the gods being a spirit of command does sound good, although command doesn't sound very emotional, he could be angry people aren't doing what he said anymore i guess? The Command Spirit in DAI was annoyed the physical world wouldn't follow it's commands so maybe it would have become a rage demon if you hadn't helped it? Maybe? A Valour spirit being an inspiring leader through its great displays of courage, becoming corrupted by it rage and hatred towards it's enemies feels more engaging and less petty, but whose to say Bioware doesn't want him to be petty? Either Valour or Command could work but there's another Evanuris who we know was obsessed with gaining more followers/worshippers under his command.

I'm talking of course of Falon'din, good catch on the use of "hunger" and "appetite" by the way, my brain skipped on by and zeroed in on "vanity", "adulation", and "amassing more worshippers" instead. Vanity having do with how we want others to think of us (in this case with adulation and worship) makes me think more of envy, pride or desire then hunger, though obviously the fact that I'm coming at this from an angle of "what would their uncorrupted spirit self also be" influences my thinking there since none of my thoughts on hungers corrupted purpose particularly really vibe with Falon'din. Anyways, I don't think it would be stretch to describe almost any command spirit as vain given it seems to come with an inherent desire to be regarded as your commander who you will of course follow the command of. And given dai's Command spirits stubborn refusal to go back to the fade until something follows one of its commands (incidentally one of the other things Solas said about Falon'din is "most tales paint Falon'din's stubbornness second only to his self regard."), it would follow to me that a more powerful command spirit would want that on a larger scale. And that when corrupted it would want to expand its influence and be willing to invade, slaughter, & oppress to achieve that. I'd guess as an demon of Oppression/Tyranny - but desire, envy, and pride might work as a corrupted command spirit wanting more followers too.

June is basically a complete guess since we know bugger all about him. The dalish call him the god of crafts, and his temple of Mythal mosaic had an anvil while Sylaise's 'anything they can do i can do better' song said her "skill rivals June's craft". So he makes something. Obvious guess is spirit of creativity, which supposedly doesn't exist because spirits aren't supposed to have creativity, though i think the whole Pantheon breaks that rule, ditto Cole and Audric. Ultimately he could be anything, though prominent demons that I haven't covered with another Evanuris yet are sloth and despair.
So... Creativity>Sloth as metaphor for writers block?

We know so little about them all that I wouldn't be surprised if these guesses all turned out to be wrong but it's fun to speculate.