The whole electrical circuit is software controlled, to suppress fuses, so you have to be carefull if you want to tap any additional light.
See some threads dealing with installing a trailer plug, such as
Installed a hitch and wiring harness on my M3
One solution that I would considere could be to replace the rear reflctors with
custom LED, that in general is used as additional braking lights.
Having the rear fog light at the same hight as the front fog lights, would be even a better design than using the reverse light.
The major trouble would be to remove the rear bumper.
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