The ground to the frame in the photo below is the last ground to frame that Ford used on your F53. The plug in the photo by it is all of the power wires to the rear on the coach lights with no ground.
From that point to the rear lamps was wired by the coach builder and how they grounded the rear lamps is anybodies guess.
From what you say you have a bad ground return from the rear lamps to the frame where ever the coach builder grounded them.
Fleetwood may be able to tell you were they grounded them.
Sounds like the brake lights are trying to ground through the turn power wires and when you put power on the turn wires the brake lights are cancelled out.
The plug is located on the drivers side frame rail by the rear of the fuel tank.
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