My turn signals have only ever blinked fast on a rental trailer with no ground wire. Rental trailers with a ground wire have not blinked fast. It could have been that all the trailers without ground wires also had crummy trailer light sockets, but I doubt it. I always assumed that you can't depend on the hitch ball or safety chains for the ground circuit.

The fast blinking is simply the electronics responding to the high resistance (same as a blown bulb).

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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