Do you have a remote start/stop in the engine compartment? Perhaps the buzzer is to warn of low oil pressure or some other condition. If it was a backup alarm, I'd expect it to only be energized when the transmission was in reverse.
Use a jumper wire to test your tail lights, see if a good ground connection makes the lights brighter. If so, then you know you'll have to track down all grounds and clean them. If a good ground doesn't brighten the lights, then take voltage readings and see if a bad connection somewhere in the lighting power circuit is robbing you of power.