Call your dealer to see if they have the OE wiring kit (separate from the hitch kit).

The E Trailer part can work, but it isn't specific to BMW. It doesn't plug into the module holder, you have to splice the individual wires in. It also doesn't disable the rear PDC.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue