I have a 2000 Durango with the ABS system. A few days ago, the motor on the ABS began running continuously, regardless of whether the ignition key was on or off. Plus, the ABS and Brake warning lights both came on.
I found that by unplugging the larger of 2 readily accessible connectors, the motor could be disabled. This also prevents the speedo from working, produced trans late shifts, plus gave me some stalling problems.
After a more careful look, found a semi-hidden connector on the backside which apparently is the power supply lines for the motor. It took a little doing, but unplugged this. Now, the motor doesn't run, and the other connectors can be plugged in, enabling the speedo, proper trans shifting, and eliminated the stalling issue. The warning lights are still on, and I'm sure the anti-lock function won't work, but at least I don't have to pop the hood and pull a connector after parking.
While I don't know the exact cause of the motor run problem (Module repair or replace likely), this procedure makes for at least temporary relief.
Maybe others can reply on the full fix, or help someone who has the same problem.