It could be a Saginaw or Muncie 3 speed,those were available "on the tree" in square bodies..
Could be someone stuffed a Saginaw or Muncie 4 speed,or even a Borg Warner T-10 in it-all would fit & work in that vintage C10,but probably never came factory with one..
I owned a '75 K5 that was 2WD and it had a factory Tremec 3 speed in it!...I almost broke it prying it off the bell housing ,found out it had 5 bolts to the bell housing instead of the usual 4,hidden up above..
I put a 4 speed Saginaw from a '75 Vega in it,bolted right in,but I had to retain the crappy Vega shifter..
A friend had a '82 C-10 that was a short bed ,owned by a telephone company,it had a factory 5 speed in it,one much like a Monza had,with the shifter built into the tail housing--it was ordered factory that way,we found the build sheet behind the seat springs..the elderly friend wanted an automatic so I helped him put a TH350 in it..
I imagine that tranny was not very rugged!..
Another possibilty is it might have the A833 Mopar 4 speed overdrive transmission--not sure what years got them,I know some 80's diesel trucks had them as an option..