Likely not making contact to metal or the hitch itself isn't grounded due to the powder coating. Could try to touch ground wire to the larger bolt just to see if its making contact. Why 'they' told you cant use trucks ground wire beyond me, less why recommending 12ga.
I gather the included harness does not have a continuous ground wire, short pigtail at both ends, otherwise you'd simply plug it into a 4pin connector.
If the ground wire from light will reach, tap existing ground wire.
Alternatively and what I'd do, you could run a wire between both light ground pigtails to white ground pigtail at plug making it continuous from lights to plug, so when plugged in wala you have ground, no bolting.
