Do you have a multimeter?
FWIW, on many BMW vehicles, there isn't a simple direct connection to a specific thing like a lamp. IOW, they tend to multiplex some of the signals, and put a small circuit board at the point of use. This means that they can supply power to more things at once, and use smaller ones to signal the board to tell it what to do and where to apply that actual power. This is one reason why there is a delay between your actual pressing a button and the function occurring...there are computers in between and logic boards. The backup light circuit may not be able to handle any more current than the anticipated bulb, if you can find where that is actually switched.
Be interesting to hear how you make out. I know it was not very simple dealing with my other BMW on a similar endeavor.
Keep in mind what functions are available in the rear panel:
- brake light
- (often, on a BMW, a separate line for the center brake light)
- running light (may be common with the license plate lamps)
- turn signal
- fog light (not utilized in the USA, but can be by swapping the switch and coding no additional wiring required)
- system ground
- backup lamps
That's more lines than shown in that plug, which is why I stated there may not be a dedicated line for just the backup lamps.
2011 535i x-drive GT, 2014 i3 BEV