Yeah, I use a LED adapter, like the Curt 57003 with my factory harness, module, and trailer with LED lights... Works great...I'll see if I can find exactly which LED adapter I have.. I know it is a 7-way to 4-way LED adapter.

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'99 E39 528i 5-speed 130k
'06 325Cic auto 115k
'05 X5 3.0 auto 173k-SOLD
'03 530i - manual swapped - 430k miles - Parting