You might get better results if you reposted this to the ZR-1 Forum. Us plain ole C4 types might be reluctant to jump in. Although your dash may be the same as any other '90. If so, I'll take a shot and ask for more info:
1. Do you see any difference whether your headlight switch is on or off ?
2. Do you have a small window at the upper left of the dash, near the headlight switch? If so that is the daylite sensor. Try shining a bright light into it for 15-20 seconds or so (with the headlights ON). Does that make any difference?
3. Do any lights on the panel work (Radio, A/C, Turn Signal Indicators. High Beam indicator, fuel gauge, Babe Alert, etc.)?
4. Do any other interior lights work (Courtesy, Console, etc.)?