I have a 2014 F550 flatbed. Two weeks ago reverse lights were on bright when truck was off and locked. Unlocked and started truck put it in reverse then drive (D) moved it 2 feet and problem fixed. This did not happen again and figured it was something to do with reverse. Today turned truck off locked it and reverse and brake lights came on very dim. Unlock started truck turned headlights on and all rear lights brake and reverse are out. Turn headlight switch off with truck running and brake light and reverse on dim. No electrical work done to truck as far as wiring goes. One month ago put a battery in truck everything working fine. Only work done on truck.

 

First thing to check is the wiring to the rear lights. Being it is a flatbed, I am going to assume the rear lights were not wired at the factory, but wired by the body builder (whoever put the flatbed on it). I would check their wiring and their splices, and check for the ground and make sure it's not corroded.

 

Check your battery to body to engine block grounds to make sure they're all clean and tight.