Well, that’s a unusual one.
Bad ground or a bad turn signal switch maybe?
But first are you sure it’s the brake lights that are working? Are they nice and bright or do they look kind of dim like they might be working on the running light filament?
Sounds like they should be working correctly because you say they work when the other lights are on.
But I figured I’d check because I’ve seen that before when there was a bad ground at the taillight.
I’m glad you mention trailer wiring. But be more specific.
Does your bronco already have some kind of trailer wiring installed and spliced into the rear harness? Maybe one of the fixtures is failing and doesn’t work well when there is the vibration from driving.
Probably a longshot, but at this point everything’s on the table.