Verified answer

Sounds like a bad connection at the fuse panel or a bad ground. Some of those cars use a common ground. In other words the ground for the radio, heater, dash lights, interior lights and so on, are grounded at one point in the car. Usually the firewall.

My 88' IROC-Z has the same problem which turned out to be the headlight switch. The instrument panel lights cut out sometimes and i have to fiddle with the switch to get them to come back on. When you twist the switch it should control the brightness of your instrument panel, all the way counterclockwise should be as bright as possible. If that turns out to be your problem you can either get one from a donor car at your local junk yard or pick one up online for probably about 20 bucks.