I've been dealing with/diagnosing the same problem in a 2002 Sable just this week. A Google search of "door ajar light" shows the usual solution is to spray a very generous amount of WD40 or similar into the door latch. The door ajar switch is attached to the door latch, and if the latch gets gunked up the switch gets stuck and keeps the dome lights on, and in our case the puddle lights on the mirror.
Another solution is to disconnect the switch for that door. Of course the interior lights won't come on when you open that door if you unplug the switch. To do this, remove the door panel. There are 2 plugs near the door latch. The 1st, and easiest to get to is for the power locks. Closer to the latch is the door ajar switch. You might have to remove/loosen the door latch to get to this one easier. You'll definitely have to remove the latch to replace the switch (about $15). Unplug the switch, and that door is now out of the system and will no longer cause the courtesy lamps to come on. This is what I did with the Sable just last night. Explorers and most modern cars use the same type setup. I think lubing the switch probably fixed the problem, but we wanted to be sure in this case.
