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The big yellow wires from the battery would be the first thing I toss.
I would put a 1/0 cable in place of them that runs from the live side of the passenger side fender solenoid to the terminal on the relay which now houses the two yellow wires.
Check the white wire on the relay, and the black wire on the controller for a silod, concrete gound.
Also, make sure that the red wire is giving you a SOLID 12 volt.....with enough amps to hold that relay open allowing current to flow.
The two smaller wires that go to either side of the resistor...are they reversed maybe? Giving it a false reading and causing the controller to think the plugs are heated already?
I made this diagram from a little research, but I have not checked it to what I have done to my truck...so if it is off, please forgive me.
Could there be a dead short in the GP harness from the resistor out to the GP's somewheres?
This is a relatively simple system, but it sure is screwing with us!