The dimmer switch has (3) connections, (2) are through the rheostadt to vary the dash lite voltage 6-12V. And the (1) is for grounding for turning on the Dome lite. Pull off the 3-wire connector see if there is 12V there when the headlites are turned ON. Most of the dash lite problems are due to a dirty rheostadt, a good solution is to simply jumper this..
Since the dash lites are that bright to begin with. This can be done with a simple jumper wire lead in the connector. Then run a second wire back for the Dome lite grounding terminal.

Just my $0.02...