1993 Mazda Miata SE anti-brake lock light is

Yes, I am a long time miata owner and part tie mechanic --

The problem is likely to be either a wheel speed sensor or the abs unit. To troubleshoot this, here are the steps you should follow:

1) check the voltage of each wheel sensor at the wheel to ensure it is within spec. If any of these are faulty, replacement should cure your problem. consult a repair manual for the specifications.

2) If not the wheel sensors and all wiring to/from them is OK, then it is likely your main abs module/ecu/brain is damaged. sometimes you can buy these reasonably from a rebuilder like modulemaster.com

You probably don't want to hear this, but this is one of those times that it will probably pay to take it into a shop as these parts are all expensive and you can throw a lot of parts money at this without fixing this. find a trustworthy mechanic and save yourself some time and heartache.

either way, the above advice will get you on the road to having this fixed.