The trailer module essentially tells the vehicle a trailer is there if the harness is connected. In addition to the features mentioned, it enables the vehicle to use the Trailer Stability Control mode of the DSC. I've never had TSC intervene, even towing on snow covered roads, but it is nice to know it is there.

Depending on your vehicle date of manufacture you may require coding to get the vehicle to recognize the trailer control module. That started with vehicles built from 2004 onwards IIRC.

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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