'Gear oils' come in GL-1 through GL-5, roughly corresponding to increasing levels of sulfur-based 'extreme pressure' (E.P.) additives (why GL-5, in particular, smells bad). Lower GL numbers are not suitable for hypoid gears--at least, not for long--due to the extreme shear forces in such applications (typically, differentials). My old tractors call for GL-1 in their gearboxes; the only GL-1 I could find was from NAPA and had to be special-ordered (5gal only). I had a discussion with David Nock about using GL-5--e.g. Redline 85W-90--in Healey diffs and he said all he's ever seen is some blackening of the bronze bushings (I think they're in the spider gears; haven't had one out in a while).
If it keeps you up at night, use your favorite engine oil in your gearbox/OD. I used 20W-50 in my BJ8's gearbox/OD for years, until I tried MT-90 to see if I could get quicker OD engagement, but was surprised that shifting seemed smoother. Since then, all my manuals--4 of them, not counting the tractors--got synthetic gear oil as SOP. It does leak a bit more, particularly at the big brass cap on the OD where the magnets and strainer are. The last fiber washers I bought for that application appeared the be thinner cross-sectionwise--more shrinkflation?--and seem to allow more leakage.