The Tocharian B verbal system is incredibly convoluted, and I can assure you, that there's absolutely now way I'm going to be able to discuss it without making mistakes. Nevertheless I'd like to give you guys a taste of what it's all about, just so you can have some nice linguistic nightmares.
There's two sets of endings, just like we like it. The Present and the Preterite endings.
The Present endings aren't exactly straight forward but do derive from the original mi-endings.
1sg. -u, -m < PIE *-oh2, *-mi
2sg. -t < PT *-tə < PIE *tu. That's right the pronoun was used for the suffix. This is because the original ending -s > **Ø. (si would remain as **s though, no -i suffix was used.)
3sg. -n, -Ø < *et the -n was added for some kind of reason.
1pl. -m can't come from *-mes looks like *-m + pronoun *ues-
2pl. -cer < PIE *-te with random -r (probably from medium)
3pl. -n < *-nt while the Tocharian A variant comes from *-nti.
As you can see almost none of these go nicely :D Nevertheless this paradigm looks more like the mi-endings than the perfect endings. The distinction between primary (-mi, -si, -ti) and secondary (-m, -s, -t) endings is severely blurred.
the Medium forms are only slightly less confusing
1sg. -mar < *-mh2+r
2sg. -tar < *-th2+r
3sg. tär < **-tr The suggestion was that it is from *to+r where -o was removed for it is used as a preterite marker. I agree it's not very convincing. But it's the best we have :D
1pl. mtär < *-medʰh2+r
2pl. tär < *-dʰue+r
3pl. ntär <**-ntr from < *-ntro with o removed because it was the preterite marker.
Let's now discuss the preterite endings
1sg. -wa < *-h2e with some odd -w- infix.
2sg. -sta < *th2e with an odd -s- infix.
3sg. -Ø < *e
1pl. -m < same origin as present-subjunctive endings
2pl. -s < unknown origin seems similar to Hittite hhi-ending -s-ten while mi -ten
3pl. -re < PIE *-ro
1sg -mai < *-h2+i and a m infix, probably to make it more similar to present.
2sg. -tai <*th2+i
3sg. -te <*to
1pl. -mte <*medʰh2+o as preterite marker
2pl. -t < *-dʰue
3pl. -nte < *-ntro without the r because r was a present marker.
Well that starts of nicely doesn't it? Present-subjunctive = present-aorist endings Preterite = perfect endings. The problem is though, that the stems themselves behave quite differently. Present comes straight form the PIE present, but both preterite and subjunctive seem to want to come from the perfect, while other subjunctives seem to come from the aorist.
But more about the stems soon, for now, just have a good look at the endings