Well that is some good detail.
Not withstanding Steve's recomendation to test the MFS, I woudl take a slightly different approach.
Remove both rear bulbs, and see if the CHMSL still has the same problem, and check if with the parking lamps on, that the fronts are on the low element, and if you use the turn signals, or 4 Way, that th efront flash ( albeit quickly due to limited load ).
With the slightly brighter, I am guessing at a bad ground on the rear of the truck, and the stop lamp is where it is deriving ground from ( via the CHMSL or BOO switch ).
Removing both the rear bulbs will stop any ground finding.
Question on the flat 4 under the rear bumper, is this part of the factory system, or an add on kit, or DIY add on ?
Trying to figure out if it is using the trailer tow circuits in the truck, or the actual truck lights ( should not be ).