this is a good one to keep you baffled huh?
here it is don't laugh....change transmission filter and fluid. when the fluid gets bad it seems to get sludgy and only flows one way! foreward. when it heats up,the fluid turns thinner so it will go into reverse.
sounds funny huh? but my 1979 cadillac fleetwood brougham did the same thing.
I changed the filter and fluid in the tranny and wow! it went backwards really good!