Connections that rely on the hitch ball for ground may not be intermittent, as there can be paint and so on in the way). A quick way to test it is to run an independent ground wire (ie a new temporary 14 gauge wire or so) from the vehicle chassis to the trailer chassis (using alligator clips if you like) and see if it makes any difference. If not, then your ground connection is likely fine. But it happens often enough that it is something to eliminate before moving to the next step.

I had a rapid turn signal on an X5 with trailer such as you would see with a bulb out. A jumper wire fixed it, indicating that the factory harness was using the hitch itself for the ground path, and not altogether successfully.

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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