Good improvisation. Appreciate the info as I'm considering installing a hitch. I don't have answers to your electrical questions, but have some info for future reference to anyone doing an install in the future. It appears that you also have the Sport Package with the body color bumpers. It appears that BMW makes a replacement for the black, bottom trim strip for X3s with trailer hitches. If you go to
www.realoem.com/bmw/select.do , enter the last seven of your VIN, you should see a screen with all the data on your X3, go to the bottom of the screen and click on "browse parts", click on "51 Vehicle Trim", click on "51 15 Bumper", go to the bottom set of pictures and click on "Mounting parts for M Rear Bumper Trim". This parts list shows the bumper parts with and without the trailer hitch.