There was a dealer accessory for the back-up light switch. It was a universal fit for both column shift and floor shift. It came with the hardware to install it either way. A bracket is mounted that holds a spring-loaded push button switch. A lever is mounted on the shifter. When the shifter is put in reverse, the lever pushes in the button on the switch and connects the circuit to turn the lights on. When the shifter is taken out of reverse, lever moves and the button pops out to disconnect the circuit and turn off the light.
You can usually find the kits on eBay, but I don't see one currently listed. If you can see the kit, what I wrote above will make more sense.
They could be wired either through the ignition switch so that it would only work with the key turned on or to a non-ignition power source so that it could work without the key.
The kit did not come with a relay. It was wired direct. When I wired the back-up light switch on my '57, I ran an ignition wire to a relay and a separate fused non-ignition wire for power. That way, it only works with the key turned on but has a power source that does not run through the ignition switch.
Matt
