I strongly suspect your problem is pretty simple to solve.
In my car (Jan,'72 build), I do not even need a key to test the back-up lights. My lights are on a constant hot. No keys needed. That's why we can forget and leave lights on and return to a dead battery.
But to get power to the back-up switch, I do need to flip my light switch on - just parking lights will suffice. Why design a car to have back-up lights go on when the rest of the lights are off? Then to have the lights turn on, the car needs to be in reverse so the switch can be closed.
See if this does it for you.
Larry
If Husker is referring to SOBill's diagram, as below, it does appear key must be on. But that is not the case for my car, and I believe others have also found this to be true.
I'm emailing Bill to get his thoughts on this diagram.
