I replaced all of my interior lights with LEDs a couple of weeks ago. Today I opened the glove box for the first time and that LED was flickering like crazy which is essentially LED failure. Now, when I took the bulb out before I did notice it was quite warm despite only having the glove box open previously. The bulb was also black. I tried to see if the light was actually being switched off but couldn't quite tell so I assumed it was and left it alone. Well it wasn't. I don't know how long it's been like it and I'm surprised the previous bulb hadn't blown but it seems the glove box light was always on. Not sure if there's some kind of failsafe to stop it completely draining the battery, but a bit worrying nonetheless (I remember my parents cars not starting due to interior lights being left on).
I pulled the LED back out today and the unit has actually melted and sagged down. Hope this doesn't happen to the others like the footwell lights which are actually supposed to be on constantly.
Now not sure if I'm going to bother trying to fix the glove box light switch or just live without the light. Might be worth checking yours especially if worried about battery drain.