Have you measured a current between the door switch and the light bulb, and between the door switch and the wire feeding the lamp assembly? If you have power to the assembly that switches on and off with the door switch being activated, but not to the bulb, I suspect that the dimming circuit (often a capacitor) has failed. If you have no power to the assembly or the bulb, I would guess it is a wiring problem between the switch and the assembly. Also, check the fuses. I don't know if there is a fuse between the door switch and the overhead lamp, but it may be something that simple, and the simple things are worth checking first. Good luck!
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