I got it working! That makes me so much happier than it really should.
I was going to post a writeup with pics incase anyone having the same problem stumbles on here, but I seem to have used all but 16kb of my photo allowance on here (unless I'm doing something wrong).
Anyway, I pulled the translucent cover off and used a scrap of speaker wire to short the circuit between the bulb and the "door" contact. The bulb lit, so that told me the problem was somewhere between those two points. I grabbed a sharp flathead screwdriver and scraped the two contacts down to shiny metal, and viola!
So if anyone else is having problems with their ceiling light not coming on in the "door" position, but other door activated lights coming on fine, try cleaning the contacts in the switch.