The ABs system on first gens are made up of % main components, ABS computer, HCU(hydralic control unit), front wheel sensors(one on each side), and rear ABS sensor. I have a bar HCU or have air trapped in it, you need a special tool to bleed the HCU and it is very hard to find. So you generally have to bring the vehical to a dealer to have the HCU bled properly. What makes the HCU so special is that there are 6 small pistons inside the HCU, 2 control front right brake, 2 control front left, and one for each rear brake.These pistons have to be opened individually to be bled properly. Hense the special tool. On each front spindle there is a sweel sensor those can go bad or get messed up from the exciter teeth on the rotor. Your rotor has teeth on the inside that your sensor picks up and esentially tells the ABS computer how fast you are going and then the computer knows how much brake to use. If you have broken exciter teeth this will throw off your ABS. The rear sensor is kind of genaric since we dont have rear disks brakes, i dont know hbow to tell if they are bad, but a new one is $15 at a auto parts store.
I would find a local auto parts store that does free ABS testing, I know autozone and Orilleys does this, if they have the tool and it is not rented out or whatever. You can only do this test when your ABS light is on, and if you shutdown your car it will reset the computer and the light will go off. So have a friend stay in the car and leave it running while your ABS light is on and ask if they have a ABS code reader and it should tell you the code and you can diagnose from there.
I have had severe AbS problems and have done a ton of research, I hope this helps you better understand how the ABS systems work on the 1st Generation Ford Explorer.
I forgot to mention if you have a dealer bleed your brakes it usually cost $200.