My 2010 F150 Ford built-in BRAKE CONTROLLER does the same thing if I am not driving at least 10MPH. I thought I also had a problem with the Brake Controller and took it back to FORD for maintenance.
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The FORD built-in Brake Controller is very much under control of the FORD computer electronics and monitors all kinds of thing during it normal operations.
This was also disturbing to me when I pulled up to a stop sign with my foot on the brake pedal expecting the trailer brakes to be engaged as well... Now that I know about the 10MPH rule I have to operate the BRAKE CONTROLLER Thumb Slider Switch with my right hand if I want to lock down the trailer brakes when setting at a stop sign...
I suspect this is what happening to your setup...
Does your brake pedal action slow down your trailer when going over 10MPH.
When I use my SLIDER SWITCH I provide maximum DC Voltage going back to the trailer brakes. When using the Brake Pedal the trailer brake voltage adjustment comes into play... I think my setting ended up being around a 5-6 Number using the + and - push buttons on the controller to make the adjustments...
Roy Ken