Your problem shouldn't have anything to do with the brake controller. The power to the electric trailer brakes comes off a different "pole" on the truck plug than the right brake light does.
As far as I know, the RAM wiring comes with a 7-way RV plug, and a 4-way flat plug. If you have a 5 pole plug for your boat (which I have as well), that 5th pole is for the reverse lights, and it turns on a solenoid so that you can back up without your surge brakes locking up.
So, are you using an adaptor to plug your boat in? If not, how are you doing it?
I'd also suggest checking to see if your right turn signal works. If it does, you might have a grounding issue.
2012 RAM 3500 Laramie Longhorn DRW CC 4x4 Max Tow, Cummins HO, 60 gallon RDS aux fuel tank, Reese 18k Elite hitch
2003 Dodge Ram 3500 QC SB 4x4 Cummins HO NV5600 with Smarty JR, Jacobs EB (sold)
2002 Gulf Stream Sea Hawk 29FRB with Honda EV6010