Not up on the different trailers nor did you say how old your trailer is. Nor did you say if you have pulled this trailer previously with no problems.
Personally, I would start with the simplest inspection first. As the Etrailer link stated, check for corrosion and/or a wire shorting to ground. I would visually inspect the wiring from the trailer plug to the brake wiring going into each wheel. If no problems found, then start checking each brake assembly by pulling the drums for problems.
2015 F350 Ultra Lariat CrewCab Long Bed 6.7L
2005 Keystone Outback Sydney 30FRKS