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If your 63 is like my 65, the dome light wiring is part of the rear harness which plugs into the main dash harness behind the instrument cluster, up high over the driver's left knee.
Do the courtesy lights under the dash work?
If no, then you may have a bad fuse in that circuit.
If yes, then either the socket is bad, one of the 2 wires that snap into the socket have come loose, or the wires may have an issue at the rear-to-main harness connection.
The dome light socket plugs into the harness with 2 bullet-styled terminals. You should be able to remove the dome light from the halo panel and see if both wires are still connected.
My 63 coupe had the same problem. When we noticed the brake lights were not working we found a poor connection at the fuse. Just moving it around fixed it. This corrected the brake lights and the dome light/interior lights. I don't know if they are supposed to be on the same circuit but they are. check for a blown fuse or poor connection at the fuse. I think mine was the second one up from the bottom.
Tom
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