reverse lights not working

First check if the bulbs are burned out. If they are okay, this is likely to be a dealer-only item. BMW is extremely stingy when it comes to giving out their service information. The only thing shown on the wiring diagram is the instrument cluster feeds a lighting module, and that module sends twelve volts to the backup lights. Nothing is shown on the diagram related to a backup light switch or transmission range sensor on the transmission.

There is a range sensor on the transmission for automatics, but I suspect if that had a problem, there would be other transmission-related problems.