Thinking out out loud here, may be way off base:
If the ground wire attachment for the tail lamps (on one side) has detached from the chassis, the brake light circuit may be finding ground through the light bulb(s) and circuit for the other lamps at that corner.
All the bulbs at one corner share a ground point.
If that ground is not connected, the circuit would go through the other bulbs and dimly light them up simultaneously as they complete the ground side of the circuit.
So I would check the ground side of the right tail light.