Welcome to 2CarPros.
What you described is textbook for a bad or weak ground. The dim light and the idea of power back feeding to the signal light in the vehicle. I would suspect a bad light socket causing the interior light, but the idea of it getting dim really leads me to believe it is a ground issue.
The first thing I suggest is to check the condition of the light socket in the rear of the vehicle. Make sure it is in good condition, not corroded, and there is nothing causing a short. If that appears good, confirm the front as well.
If both lights and sockets are good, then we need to check for a bad ground, which is my first suspect.
I attached a portion of the exterior lighting wiring schematic. I circled the light in question as well as a ground splice and where it mounts on the body of the truck. I highlighted the ground wire. If you find the sockets are good as well as the light bulbs and the bulbs are the correct ones, the easiest thing to try is make a new ground. Take wire and basically make a jumper between the socket ground and a known good ground on the truck. Then check if it fixed the issue. Other than that, you will need to trace the ground from the light socket and inspect it for breaks, check the splice to make sure it is tight and clean, and then inspect the ground itself on the body. If all of that checks good, then check that wire for continuity. If you note, the splice (S427) is where both lights attach. If the ground is interrupted, rather than power flowing to ground, it can find its way to the interior signal light.
This sounds a lot harder than it is. Let me know if you have other questions or let me know if that is the problem.
Take care,
Joe
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Wednesday, September 4th, 2019 AT 7:55 PM