2001 Ford Explorer - Glove box lamp remains lit all the time. Any secrets on this one? Unable to remove lamp.

If I remember correctly, it has a black post that when you close it, it pushes it in right? If so, maybe the glove box is mis-aligned, or the post is broken off to some degree. If not visible, may be on the top behind the glove box. I remember having this problem before, and have been around a lot of Explorers. If I see one at a used car dealer, I'll go look!

I have the same problem. I unplugged mine, as I assume the switch is bad, though I'm not sure what it looks like or where it's located. I don't believe it's the normal pin switch, but rather part of the latch mechanism.
You'll find the light under the dash above the box. Open the box and push in both sides and it will drop down so the light will be in plain view. There is on wire leading to the light and it can be popped out with a small screwdriver.
At least the light will not be draining your battery.