You have described perfectly the classic symptom of a bad ground. To verify it, turn the head lights off, turn the right signals on, and you will find the left rear signal is also flashing dimly. If you remove the left rear signal bulb, the right rear bulb will stop lighting up.
I have to qualify that last statement. The right bulb's current may still be finding a path to ground through the license lamp. Regardless, it's the ground wire for the right rear lamp assembly you need to look at. Some bulb sockets use a push-in ground terminal that is noted for corroding. There could be a wire that got cut from something rattling around in the rear. A splice could be corroded. If there's a trailer wiring harness and someone used Scotch-Lok connectors to splice the wires, those do not seal out moisture, and corroded wires are the most likely suspect.
Sunday, November 20th, 2016 AT 2:42 PM