I've always thought of doing a Caucasian timeline, but I've always been doing other things.
What I know about the Caucasus is that it's inhabited primarily by various 'Nakh' peoples. These people are mostly Muslim, and Islam was brought by travelling Arabs, not conquering Arabs. The mountains kept the area relatively isolated though, so Islam developed there with significance elements of older beliefs, kinda like in rural Albania.
Apparently they mounted stiff resistance against the Russian advance into the area, and were skilled guerrilla fighters. They had a few charismatic Imams try to carve out states. This suggests to me that religious identity was significantly more important to the Caucasians than ethnic, national, or tribal identity, which makes sense, considering how isolated it was from the European concepts of nationality.
They have a long tradition of poetry, apparently. Also, while Georgia, Armenia and Azerbaijan are considered the Caucasus states, there are lots of Caucasian ethnicities in the Russian federation. Azerbaijan being a Caucasian nation is arguable (its in the same situation as Estonia, being culturally different, but geographically Caucasian).
Basically, there aren't many TLs on it, because Westerners usually don't factor it into their worldview. It's the Russians' playground, the West has never had very many interactions with the Caucasus, and the Russians have suppressed the peoples there. So, a similar situation to remote, largely native-inhabited parts of Mexico.
EDIT: also, North Caucasian Islam was more politically-charged than normal, being used to stiffen defense against the Russians. It's pretty lax, with tobacco and alcohol pretty popular. It's highly syncretic, and they refer to God as Deila, the head of the Vainakh pantheon, rather than as Allah. The Avar imams didnt like Chechens, considering them unreliable. Apparently sharia law clashed with adat, the indigenous law system that the Chechens considered superior.
Highly mystical Naqshbandiism was also very popular, apparently. There aren't many English-language resources on the Caucasus really, and very few books.