Tail light stays on

I have a '71 Dart Demon. The left tail light stays on all the time. The other lights work as they should. Can anyone give me an idea what the problem is? Thanks

I would start by grounding that light socket to a good ground.
Temporarily touch a wire to the socket right at the bulb and to the bumper or body metal.
These cars are notorious for back feeding power because of bad grounds.

Then pull the drivers kick panel and make sure it doesn't have a short between the trunk light wire (always hot) and the tail light wiring, (they share the same connector) and then if that isn't it work my way forward up under the dash following the tail light wires till I found where that tail light wire was crossed with power.

A 12v test light works well for this.