I think combining TTT and Kellhus' internal mystery voice into one thing is folly.
TTT is not an entity itself, its a thought. Multiple people have grasped it, even the half Dunyain. I believe Maithanet, inrilatas, and kelmomas all grasped it. There might even be hints in the Survivor sections of some grasping there, but I might be making that bit up.
Granted, the explanation that the Thought just talks to whoever it want explains this as well, but it seems that there would be more than just a bunch of crazy dunyain half-breeds and their parents that this sentient Thought thing would reach out too.. No, I think the common denominator is the probability trance, Occam's razor this and its just an extension of that. (Occam would not have done well with musing about these books though
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Nah the voices and the thoughts are separate in my view.
The thought is the predetermined actions, I don't know what the voice is, so many people hear them, it might be different things.
Some people know it's name, doesn't mean they have grasped it. Esme knows it's name, she hasn't grasped it. I cannot recall any evidence that any of the named people have grasped it, beyond knowing it exists and naming it.
As Richard Feynman says "You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird... So let's look at the bird and see what it's doing -- that's what counts. I learned very early the difference between knowing the name of something and knowing something."
Again the Thought is separate from the voice in my crackpot interpretation.
For instance I think Little Kel voice is ultimately a tool of Kellhus. Since we're also talking Malazan in the quorum as i type this, he was kellhus "shaved knuckle in the hole" against the white luck warrior.
I'll need to get all my TGO "revelations" written down before TUC, used to having more time to spread it out. A titbit is i think it's the real Lord Kosoter who mouths fungal warnings from Kellhus's belt :O