I agree with where Mike is going on this. I also suspect the problem is somewhere in feeding power to the instrument panel lights. It would be a good idea to start tracing and checking wires starting at the light switch, checking for power also at the panel dimmer switch, all the way in to the cluster. Also check to see if you have park lights, as that could be another piece to the puzzle.
Interior lights can still come on, even if there is a problem with the panel dimmer.