On my '08 Dodge, the light wires ahead of the jack are only 18ga. If you plug in a trailer with a few extra clearance lights, that's putting a real strain on the watts.
I'm rebuilding a camp trailer now and it's getting all LED lights just for that reason.
A couple years ago, I replaced the light jack on the truck, too. The stock one gave me all kinds of fits. Before you spend a wad at the dealers, check the brake wire ahead of the jack to see if you have good power there. It could be a problem in the jack.
If it's bleeding power when you don't have pressure on the brake pedal, it's got to be in the brake controller. You will have constant full power to the controller but there should be none after it until you push the brake. Also, check the emergency brake pedal if it has a switch to set trailer brakes. It might be sticking slightly on, enough to give you a drain.
