The length of the case might be one way, and there might be identifying numbers cast into the case as well. But there may also be a difference in first gear ratios that might clue someone in that knows that kind of stuff.
So along with the measurement you already provided, verify the first gear ratio by shifting it into first and spinning the input shaft by hand, while counting the number of turns of the output shaft.
Seems like there is a 2.99 to 1 ratio, and a 3.20-ish(?) to 1 ratio, and maybe one other.
Good luck.
Paul