"IF" the trailer connector is in good shape the next thing I'd check would be the headlight switch connector. You have to remove the dash bezel. It just pulls off AFTER you remove the one screw on the top right (mine is inside the little door for the aux power outlet) I understand that if you have (those stinking) road lights switch is in the same place. Anyway, pull the bezel off, with an automatic it's best if you have the shifter in the 1st gear position (lower down). Then the screw(s) on the headlight switch face plate and you can pull the headlight switch and connector out of the dash some. If the plastic connector is melted it could be letting your wires touch each other.
If this is the case you can either get a new plastic block kit from the dealer or like I did (and the problem has never come back) is to put individual crimp connectors on each of the wires (make sure you make a diagram to put them back in the same position). Lastly, the heavy 10 gauge wire I soldered to the crimp splice (after cutting off the plastic sleeve). Now the switch is always cool to the touch. I hope this corrects your problem.
Attention: TDR Forum Junkies 
