Hi,

I think if you look into any manual for your year car, you will find out the back up lights are turned on by a switch underneath the rubber shifter boot on manual transmissions.
It’s on the left side and when the ring is pulled up to move the stick over to reverse the stick pushes a lever on the switch itself.
It’s all a neat package but you can have a wiring issue from there. I do not know about a relay on these cars being used at all.

I do not know how it was done on automatics but the M46 is a manual transmission and if it has overdrive it will have a button to slide right up on top.
On other M46s from like 1985, I know the knob has a push button and those use a relay to control the overdrive.

Hope this helps.

Phil