I have fixed many a light set. First thing to do is take the red reflector off both sides of your tail lights so you can see the bulb itself.
Now have someone go into the truck, and turn on the right signal and look at the bulb. If the thin filament is turning on, then you have a ground issue.
Try the other side and repeat the process. If the thin filament is turning on, then you have a ground issue.
Check the ground issue by connecting your negative jumper cable to the negative battery terminal, and then to a wire that you touch to the side of the socket. If that fixes it and makes things work correctly, that is the socket that needs to have the connection to ground from the socket repaired.
What actually happens goes like this. You send power to the brake filaments, and normally that power returns on the ground. However when the ground comes loose, the power goes through the thick bulb filament, then the only way out is through the thin bulb filament in reverse. The thin one glows brighter when they are in series. The power then goes over to the other side and goes through the thin one on that side and out on the working ground.
So, you think you have brake lights, but actually you have weak running lights.
Hope this helps.