Both Headlights Fail at the Same Time

According to my '90 wiring diagrams there is a headlight relay, located on the driver's side inner fender well. There's a bank of relays under a black plastic cover--the outboard, rearmost one should be the headlight relay--the connector should have four terminal with one White/Black wire, two Red/Blue wires, and one Blue/Yellow wire.

Hope this is of some assistance.

relay. Could this be what it is on my 1991 Miata, with 170,000, that never gives me any trouble?

controls the headlights only. All other lights working fine.

There is a fuse and a relay under the hood on the car's right side on 91 miatas. The fuse box should say which fuse is the "retractor" fuse. Check it. If you don't know how to tell if the fuse is good or not, consult with someone who is familiar with fuses. If the fuse is good, the relay in question is near the fuse box, attached to the inside of the right, front quater panel. I'd have to look at my wiring diagram at home to tell you exactly which relay it is. Tapping on all the relays lightly with the handle of a screw driver and the headlights "on" can substitute if you can't find the correct relay. If the headlights still don't come up, the only other thing I can think of that is quick would be checking the wire bundle above the accelerator peddle in the car. The wiring for your headlights is in there somewhere. I had a bad connection in there on my 91 Miata and if I bumped it with my leg with the car running the headlights would twitch. If still no luck, have someone check the entire light system with a multimeter.