The factory wiring connector is under the rear floor near the spare tire, but you won't be able to use it. It is a connection for a specific BMW module (which comes with the BMW wiring harness) that translates the multiplex signals into outputs for the trailer wiring. If you want to tap into the lights, you need to do it at the rear corner lights, or close to them.

Do you have a converter in case your trailer is different (combination brake/turn or separate)? Just follow the wires back from the bulbs. If you don't get any codes from the Lighting Control Module (LCM) for unbalanced loads then you are good to go.

Don't drill any holes, there is a large hole in the rear pan for the factory wires to go out through, and you will need a rubber grommet approximately 1" to fill it (from memory).

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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