3 speed manual transmissions were standard even in Chevy and GMC 4X4's through out the 1960's. Many if not most 4X4's had the optional 4 speed as a 'creeper' first gear is a big advantage off-roading. Most Chevy and GMC 4X4's from 1960 to 1970 used the Rockwell T221. T221's make some noise particularly at highway speeds, but popping out of gear is never normal! Parts and kits are available for the T221, but not cheap. Not sure if these guys are any good (never used them myself) but looks like they have a lot of parts:
https://torqueking.com/category/1960...transfer-case/