Thanks all. At least I'm not alone. I was using the 7-round plug which is supposed to have a ground in it.
I also had the triple fast flashing blinkers. I'm used to American SUVs which will blink too slowly but that's rectified by changing blinker relays. Might try that to see what happens.
Next step- wiring the electric brake controller then buy a new race car trailer.

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'04 E53, 4.4 Sport
'97 E39 528i
'86 911 Carrera, track car
'96 BMW R1100R