One other thing you might check is the amperage draw of your trailer brakes. It should be somewhere between 2.5 and 3 amps per wheel. Roughly a 12 amp draw for a double axle trailer with brakes on all axles. This is with your controller maxed out.
Sounds like the short is in the trailer. You have checked the truck out to no avail. My family pulls a lot of horse trailers and I find one very common problem. They always wire the trailer brakes with too small of a wire. With a heavy load they fade badly. Run two new 10 ga wires to the brakes, one to each side and solder and heat shrink all connections. Solder them together just before they go in to the trailer plug and I bet your problem will go away and you will have much better brakes too!
MotorsForum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.