So it only happens while the car is moving? If you come up to to a stop sign or red light, the ABS light goes out?
Edit: reason for asking is the ABS system on most cars does a self-check the 1st time the car hits 10MPH to ensure the pump, sensors, etc are all talking. If the light comes on after that it indicates a component is toast or at least the computer isn't able to receive the input.
Here's a link that may help:
Saturday Mechanic - Troubleshooting Antilock Braking - Popular Mechanics