Don't surge brakes generally have a reverse lockout so they don't operate in reverse? Again, no experience, but I thought I'd read that.
Trailers with drum brakes don't need a reverse lockout, trailers with disk brakes do. Drum brakes offer almost no braking power with the trailer wheels going backwards. (Google drum brake servo action.)
The lockout can be mechanical like a simple C-clamp you have to put on the hitch, a pin you install in the hitch or a Normally Open solenoid on the hydraulic line that is turned on by the reverse lights of the tow vehicle. Umm, does the FJR have backup lights?