That is very strange. Well, here is what to look at first.
Check the bulbs. I think they are dual stage bulbs. They should have two fillaments in each bulb. Check to see if either of the coils are broken. If they are, replace the bulb and see what happens.
On our mustangs, there is an ABS tester on the driver's side engine compartment. You should be able to run the test to verify that the abs system is working. Get a chilton/haynes manual for the car and run the procedure. It should also give you more information on the ABS light.
Also, there has to be some sort of relay that tells the brake lights to come on/off when you push the pedal. Look in the manual, and trace the wiring to this relay. If it went bad, that would explain the lights not coming on.
You can have someone hold the brake while you hold a multimeter to the two terminals for the "brake lights". If you aren't getting current, you have some form of an electrical problem (i.e. relay, broken wire, etc). BTW, you should see current at the two terminals for the "running lights", since they are working.
Scott