How do you determine why the brake lights are not working on 1990 Mazda miata?

You'll need to clarify if it's a single light or all of the brake lamps.

If it's at least one light, but not all of them it is typically the bulbs. Access to these is from a Phillips head screw at the top of the headlamp, under the trunk, and if you remove the interior carpetting, some bolts behind the tail lamp.

If it's all of the lights, it's typically the fuse. The owners manual and/or the fuse box itself will have a diagram of the fuses, and you can determine which one is used for brakes. There are fuse boxes in the engine bay, as well as the in the interior, underneath the dash by the hood release pull.

If you inspect the fuse and it still looks good, try replacing it with a new one anyway, just to check.

If it's still bad, then perhaps no signal is being sent:

• You can test this by using an ohm-meter and connecting the pins to the two leads where the fuse would connect.
• Another inexpensive way is to purchase a fuse tap from an electronics store. It looks just like a fuse, but has a metal tab on top that allows you to draw power (meaning that you have to plug it in the correct direction). You can connect a 12-volt bulb or LED to the tap, and connect the other end to a part of the engine to ground it.
• Have a helper press down on the brakes, and see if the ohm meter picks up a difference in voltage signal.

If you receive no signal, then it's probably the brake switch. If you look at the brake pad, and follow the pedal up, you will see a small, squarish switch slightly to the left, held by one bolt. You can remove this to test for electrical current as well.