got a 92 dx. When I have the headlights on, sometimes the dashboard lights go off for a few seconds. I can usually make it come back on by turning the headlights off and on, or if I just wait long enough, the dashboard light will come back on.

Does this sound like a loose connection somewhere behind the dash?

 

Try pressing on/tapping the dimmer switch for the interior lights - it's the little roller wheel controller to the left of the steering column on the dashboard. When this switch starts to go bad it can cause the interior dash lights to flicker, and eventually go out.

Is is just the instrument cluster lights or also climate control lights that flicker? If it's all then the dimmer is likely going to be the problem.

 

Here it's #3 in the picture - pretty common failure for 92-95 Civics:

 

I think that's what I did, actually, to get it to come back on.

I can't remember whether or not the heater stuff was going off too.

 

take your dimmer switch out, there will be 3 wires (red, black, red/black stripe) cut the red and black wires then twist them together and tape them off. Do not reconnect the wires back to the switch, just leave the red with black stripe wire connected...you just bypassed the dimmer switch