Does your traction control flash at the same time? There is a way of checking the fault codes with a paper clip. You just need to short circuit terminals E1 and Tc in the diagnostic port, if I recall correctly. Then you will need to count the amount of times that the ABS light flashes to tell what number you're getting. Btw, this information is only for the 3ES (97-01).
Replacing the brakes won't fix this issue. You will only see a BRAKE light, when your brake fluid dips below a certain level. An ABS light is completely different.
I don't have a reference for the 1993 model year, but this is what I used for my car. (1998)
Try it and see if it works, I doubt Lexus changed the system in those 5 years. Just so you know, I was able to read the codes with and without the Shorting Pin....not really sure which way is correct. Without the shorting pin, I was getting a bunch of different codes. With the shorting pin, and after resetting the computer, I was only reading one code.
p.s.: I just noticed that if your ABS light is ALWAYS on, then there might be a computer issue. Whenever I have my ABS light come on, it goes away after restarting the vehicle and only reappears under certain conditions.
The ABS light will flash multiple times, the frequency and the number of flashes indicates each digit. For example, 4 fast flashes, a pause, and 3 more fast flashes is number 43. If there are multiple codes, they will appear in a numerical order and then repeat.
Check tyre pressure, check wires (from BCM ECU socket to all 4 sensors, check every sensor impendance, check each wire relative to the housing of chassis GND), Check U-Bat (12Volts) of BCM ECU (minimum 2 wires is 12 volts, one - direct from main battery, second - from Ignition Key). If no 12 (10.5-13.8) volts - check a bigest fusses. Check a brake fluid level and sensor.
If no reasons - go to local dealer, and coonect toyota tester or techstream for detail diagnostic procedure.
With Techstream - check errors, if no errors - try activations of Brake ECU components. Check ABS motor. Maybe its jammed. If the test is not success - new error will appears.