Originally Posted by Dreadnaught

Take out the dome light housing and wiggle the wires leading to the bulb that isn't illuminating where the wires go into the connector for that bulb. If the light illuminates/flickers when you do that, that would tell me there's an issue where the wires plug into the dome light assembly. That's where I'd start next. You could also wiggle further down the wires as much as you can when you pull the dome light housing down and if the bulb illuminates/flickers you have an issue with the wires where it does so. You would need to strip the wires for further investigation.