I have a 13 GT. Does one of the dome lights stay lit dimly when the car is off? I can see a faint dim light from the passenger side. Is this normal?

 

If you didn't buy your Mustang 'new', the last owner has more than likely changed the bulb to LED or some other aftermarket bulb.

 

The lights should go completely out.

 

^ that was going to be my guess also

^ yeah, you would think, if a switch is off, there should be zero voltage on the circuit and nothing should be on. But apparently there is some kind of "soft switching" in the light circuits (maybe others too?) that leaves a small voltage in the circuit when they are off, and this is enough to make the LED's glow . . . . I guess