URGENT Problem with internal lights in Mustang convertible

Sounds like a door jam switch may have gone bad or is stuck. Look for the plunger in the door area and then work it back and forth by hand and see if that fixes it. If there isn't an exposed plunger (I am not sure if the recent cars even use a mechanical plunger type switch) then you'll just have to remove the bulbs for the short term 'fix'.

If this is a rented car, you may be unaware that there is a courtesy light switch on the dash.

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on, full left position??

Internal lights (map lights) controlled by switch on left side of dash which rotates up and down.....all the way up keeps the lights on .. rotate down and they will turn off by timer...overhead lights have their own switch....

I believe the lights are on a delay and after you close the door they go off after 30 seconds. Are you just not giving them time to go off? The other solution is to just take the bulbs out.