The problem is most "trailer wiring receptacles" have no way to properly operate a third brake light.
On my 20 F150 I had to wire from the back, with a separate connecion all the way to a wire under the hood that is a "brake light" activation circuit.
I originally did this for my RSi Smart Cap shell as it comes with a nice LED third brakelight already mounted.
BTW RSi has been unable figure out an easy means to connect it to existing wiring for turn signals etc. They've sent out multiple harnesses that don't work right.
On my ATC I just finished mounting a rear view camera at the top of the lower box, just above the door, but not on the roof portion.
That kind of leaves me with no good spot for a third brakelight. If I mount it right under the camera it probably will blind the camera at night. Don't want it on the raisable top as wiring would be a PITA.
My ATC came with side amber and red markers. It also had 2 red rear LEDs I assumed were markers but they are actually tied to the turn signals- so they sort of work as brake lights.
They don't appear to be very bright though.
The ATC has a traditional 4 wire trailer pigtail to plug in- but unfortunately it won't work for me since Ford saw fit to mount the receptacle in the bumper step well- guaranteeing it will get stepped on and broken at some point.