shor,
Didn't most transmissions come with a switch installed in the tranny to address the backup lights. I don't know if this would be the case with yours, but if so, it certainly would be more convenient than having to manually switch every time you wanted to back up.
The switch usually had two poles, and was NO (normally open). When the transmission was shifted into reverse, a ball, or plunger was depressed closing the switch and completing the circuit. They are sometimes hard to spot..covered with gunk and hidden. It might be worth the search.
Stuart