Whenever someone asks something about TAM evolution, they seem to inevitably be pointed towards the World Lexicon of Grammaticalization (Kuteva et al., 2e, 2019) and The Evolution of Grammar: Tense, Aspect, and Modality in the Languages of the World (Bybee, Perkins and Pagliuca, 1994). And I have consulted both of them. But something's just not clicking.
If you look up in either of them where the present tense can evolve from, you'll be told a number of possible auxiliary verbs as lexical sources for grammaticalization: "come", "go", "do", "be at", etc. And if you look up where the imperfect (=imperfective past) can evolve from, you'll be told... basically the same set of possible sources. This is because they both evolve through the same intermediate stage of progressive/imperfective aspect.
What isn't clicking is how, once you have that imperfective aspect grammaticalized, what causes it to diverge into two different conjugations that mark different tenses?
Like, if the imperfective turns into the present, then now how is the imperfect supposed to be expressed? Does the language just lose the ability to express it? Does one aspect marking somehow get stretched out into two new conjugations, and if so, how - what morphology would you have to add if there aren't already tense markers?
The only language I know of a concrete answer to this for is Attic Greek, where the PIE imperfective became present, but the PIE imperfective + the augment became the imperfect, and the augment transparently marks past tense, probably evolved from a demonstrative meaning "then; at that time". But the augment wasn't universal among PIE's descendants, so what did the rest of IE with morphologized present vs. imperfect do to create that?
Or in Georgian - IINM Proto-Kartvelian is thought to have been originally aspect-only, like PIE - you have present Ø-v-a-shen-eb "I build" vs. imperfect Ø-v-a-shen-eb-d-i "I was building". So this -d- is like the augment, marking past tense, right? It's hard to say so when it also shows up in the present subjunctive Ø-v-a-shen-eb-d-e and the future subjunctive a-v-a-shen-eb-d-e. So then what is this -d- and where did it come from?