1989 Corolla Overhead Light

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If your car is anything similar to my Camry, there are plunger switches hidden under black rubber covers on each door frame. The copper contacts inside them oxidize, preventing the switch from closing the circuit. I've had to disassemble each one and clean them, using a spot of hot glue to hold the switch casing closed.

Also, I have noticed that the bulb used in the dome light tends to form white oxidation at the metal ends, also preventing a closed circuit. A little light rubbing with a scouring pad should clean it off.

Clean the blub contacts first, then give each of the switches a little wiggle with your finger and see if the light winks on...if so, it's the switches. If you have a camera, post a pic of the switch and I can confirm they are the same. If so, I can offer more detailed instructions on how to dissassemble and clean them. Hope this helps!

Keep in mind that the dome light circuit is a ground actuated circuit.
Meaning that the light comes on when any of the switches are "grounded"
so you can take the switch out then ground the wire and the light should come on, if it does then it’s that individual switch if it doesn't then it’s the wiring. Probably the switches since you said at least one of them works.

Ayup...as I guessed, they're the exact same as those in my Camry. The metal plate can be removed after cutting the plastic nubs holding it on. Remove carefully, since there is a spring in there...don't want pieces flying and so you can see how it all goes back together. Once you get it part, you'll see where the contacts are discolored and dark. The contact attached to the plunger can be cleaned with fine grit (400 or 800) sandpaper, but I used a water-dampened scouring pad. A wire wheel on a Dremel tool works well too. The contact inside the plastic cup is tougher...I used a sharp knife to gently scrape it clean and shiny. Be careful to not bend it.

Drop a dab of dielectric (or spark plug boot) grease on the plunger sides and reassemble. I used a hot glue gun to put a dab of hot glue where the plastic nubs were. Trying to use hot glue and THEN reasssemble will only result in cold glue by the time you get it together. A dab at all three spots is enough to hold it...pliers are good to use to keep the plate tight while the glue cools but fingers work too.

Its been a while since I did this so forgive me if my descriptions are somewhat vague. Let me know if you have more questions. Good luck!