Even though you say you have checked the bulbs, recheck them again including the trucks- recheck all bulbs that have a brake light circuit and element.
The fact that more light come on when the brake is pressed is a clue. Somewhere the circuits are getting crossed and getting power by the brake circuit. There may be the chance that inside a dual element bulb that one of the elements broke loose and crossed over to the adjacent internal circuit. I am not saying this is the cause of this specific problem, but I ran into just this years ago when working at a dealership and it drove me nuts trying to figure it out.
Before going deeper, use the KISS principle and recheck all bulb that have a brake light activated. I am a firm believer in the KISS theory... in keeping with it, make sure that all grounding has good connection including between truck and camper.
Sold the TC, previous owner of 2 NorthStar pop-ups & 2 Northstar Arrows...still have the truck:
2005 Dodge 3500 SRW, Qcab long bed, NV-6500, diesel, 4WD, Helwig, 9000XL,
Nitto 285/70/17 Terra Grapplers, Honda eu3000Is, custom overload spring perch spacers.