I don't know if this is any help to you, concerning your backup lights. But, on my 325 , on the drivers side (left) my marker light that is half way down the side, for some reason, comes on when I put it in reverse. Weird I have LED tail lights, and my backup lights are in my bumper. Still haven't gotten them to work, I'm thinking maybe that side marker light was wired that way to let the driver know he's in reverse. I haven't looked into it future, but that wire may be the lead from the steering wiring.
Does anybody else have this thing on the side marker light? DJ