Tail light stay on

No

No power to the dome light. Another question thou. The rubber seal around the tail housing is deteriorated. When I remove the bulb from the housing it shuts off that side. Is it supposed to be grounded through the light housing?
I do not understand what you are saying here. I mean, if you remove the bulb, of course it is shut off.

EG: My 70 RR the sockets had 3 wires, so there was a dedicated ground to the socket shell. I don't know if your Barracuda would or not.

But I think we have strayed. I would concentrate on the problem first. "Where" is the tail lights getting power when they should not?

1....Disconnect headlight switch. If the power stays on, then it is not coming from the light switch

2....With the problem "showing," access the kick panel rear harness connector. Look up the wire colors, and probe all pins of the connector. With brake lights off, and key off, there should be only 1 or 2 pins active. The tail lights (because of the problem) and the dome light circuit if it works. If you can pull the fuse for the dome light circuit, that should kill the tail lights IF it somehow crossing wires in the harness.

If so, verify by pulling both bulbs, separating the kick panel harness, and then check continuity. The tail light wire should NOT show continuity to any other wire in the harness, or to ground.

If it does, the problem has to be right there in the rear harness

3..If 1 or 2 brings no answers, there is not much left. The path from the kick panel connector, at the tail light circuit, up to the headlight switch, is a short length of wire. There should be nothing else on that. If it is still getting power, trace the harness from the kick panel to the light switch.