1966 3 speed manual trans problem. Help!

FIRST THING I'd do is do THIS:

Jack it up (safely) after getting the car "pointed" lol

Unhook the shift linkage from the 1/R lever and put the trans manually into first, leaving the linkage unhooked. Now do a short test drive and see if it actually pops out. If not you have a linkage problem.

If it does you certainly have a gearbox problem, and may or may not have a linkage problem

That's a smart test.