Sounds like a bad ground... The 3rd light should be a completely separate circuit from the taillights, but it looks like it is grounding through the taillights.
Do you have a flashing third brake light? if so, someone may have grounded the flasher module to the taillights instead of wiring it in properly.
1996 Firebird 3800 Series II, T5 swap RIP 3-31-11
It lives on: Engine and trans from ^ are now in v
1996 Firebird 3800 Series II, T5