I'm only now reading The False Sun, after reading TGO. Can't believed I missed that.
Wild idea, but I'll drop it as a try.
Titirga is grasping at what shouldn't be grasped. I was immediately thinking about the Aporos and Chorae as Wilshire mentioned so long ago, and not the Daimos.
His mark is described in a remarkably different way than any description of a Mark in any of the books so far, including that of the Inchoroi, Kellhus (at least in the last chapters of TGO, as viewed by Malowebi), Akka or Cleric/Nil'Giccas.
He is very emotional, but not in a Cishaurim way, as far as I read it. The judgement in his voice, as well as the way he looks/gazes, rather parallels another character: I was actually immediately thinking of a comparison with Mimara and her Judging Eye. I remember passages in TGO (maybe already in WLW) where Akka notices differences in her behaviour. Of course this could just as well be her pregnancy hormones and/or the Qirri, but I think it's not caused by those two.
Ever since the "flashback" at Dagliash, I'm looking for more parallels/links and the one between the stories of Titirga and Mimara have one common aspect: A huge hole in the ground, in the form of the Well of Viri where one falls to the depths, his powers failing him (Titirga) and the Great Medial Screw where the other discovers a potential super-power (the revelation of the Chorae as a Tear of God) of which we don't know much yet (Mimara).
In my view, the quote below from The False Sun at least seems to suggest to me Titirga can see more than the Mark:
A lunatic God… perhaps. The Hells that you think you see. Something… Something adulterate, foul. Something that craves feasting, that hungers with an intensity that can bend the very Ground.”
[...]
Does that not trouble you?” the Hero-Mage pressed. “That you have but one eye!”