Hi,
sounds to my like there is a bad connection from (-) to the chassis somewhere. In this case the (+) from somewhere else is using the (-) connection of your rear lites and that's the reason why the stay on all time.
If you know how to use a multimeter follow the wires backwards an see where the (+) comes from. I would guess, somewhere from the ignition switch and/or light switch. There you will find the bad (-) connection to the chassis.