Decided to start a second post. I am trying to replicate and issue with trailer brakes coming on at random - pulsates like ABS and goes away
I have a set of trailer lights and a pair of brake magnets in the bed of my truck. Also ran a wire into the cab having a light bulb attached to the brake magnets.

Some interesting things I have observed. I have gain at 10 the max,

get up to speed and slow down. I watch the light come on dim and get brighter as the truck slows. sounds about right.....
Slowing down the light is now bright and truck stops - then the light goes out - but my foot is on the brake just enough the truck won't move.. not so sure about that?
Experimenting I let off the brake and push down again light goes dim to bright and stays bright until I let up the brake pedal - light goes out truck is moving
drive a few more miles and come to a stop. now truck is sitting at a full stop. light goes out. I apply the brake a little more - nothing push harder nothing - push a little more and the light goes to full bright.......

When I mention light it's the temporary one I have attached to the brake magnets....

tried headlamps on/off turn signals on off - no affect to trailer brake light - good

 

Start by borrowing another trailer and tow that. It will help you find out whether its the truck or the trailer that has the problem.

My bets are on an electrical problem in the trailer. An intermittent short triggering the trailer brakes.

 

I had a bit of trouble following the dialog in your thread, but if I understand your question about the "function" light, the brake controller is a unit that applies proportional braking force based on measuring the "G's" in deceleration. So as you slow, the current applied to the trailer brakes becomes greater as your decelerate more quickly. Once you are completely stopped, the measured G-force of deceleration is zero so there should be little to no current flowing to the trailer brakes. Pretty rudimentary explanation and leaves a lot of the technical info for you to look up if interested.

 

I agree.
if i stop with foot on brake no power because no 'G' force detected.
But if I push harder on the brake pedal while stopped it will power the trailer brakes