I've always been fond of my theory, that Tiamat gave Gith to the highest bidder, entity who wanted her the most - Ilsensine, whose thirst for vengeance against the woman who destroyed the illithid empire ran deep. Ilsensine, in return, gave Tiamat the sort of payment a greater god can give - an entire world, perhaps, or another major sphere of influence. The death of a rival. Something pretty that she can wear at clubs.
Ilsensine, after torturing Gith for a millennium, realized the best revenge possible - he implanted an illithid larva in her, transforming her into the species she hated the most. But for such a special host, only a special tadpole would do - a divine tadpole, suitable to create an illithid god. An illithid god, who consumed the soul of the being whose body it transformed to create itself.
This is how Maanzecorian came to be, and why it is only now, aeons later, with Maanzecorian's destruction that the soul of Gith is finally free.
It must be remembered that, ultimately, the githyanki (and githzerai) are "human", in the loosest sense of the term. Whatever bargain was struck between Gith and Vlaakith I and Tiamat, included obviously Gith's absence for whatever reason. I suppose that Gith herself was reasonably powerful, so she might have become one of Tiamat's favored servant in Baator, or some such. True, the "deal" for red dragon assistance (to characterize it as servitude is excessive, and some sources specifically speak of it as an equal partnership) seems to favor the githyanki, but god-only-knows what Gith herself had to offer. Vlaakith seems to be a secondary figure. Perhaps Tiamat makes the deal in the hope that (or expectation based on knowledge of the future) Gith herself, now in the "care" of Tiamat, will/may someday return to the Githyanki and bring the whole of that race (and maybe the human race as well) into "the fold", in a Power-going-for-the-big-money sort of way. Face it, humanity is the ultimate worshiper-base on the Prime. There is no race so successful or so widespread as humans. Githyanki, as a human off-shoot, are a major prize. In the long-term, multiversally speaking, they might be the only prize that matters. And if the gith races can be instrumental in the development of humanity as a base of divine power, then Tiamat may already be in a unique position to "corner the market", under certain circumstances. I mean, really, most of Western mythology is based, one way or another, on the story of the Assyrian god Marduk making the world out of the body of Tiamat..................... Tiamat's "revenge", so to speak, might be the coopting of the human race for her own ends. I digress, therefore I stop.