The "grumble" is the ABS pump working. If it's doing it's thing when it shouldn't, that suggests it is getting a bad signal. Nothing you said suggests the relay has failed. When the relay in my 945 failed, the ABS system was completely non-functional. A bad solder joint in the cluster kept the warning light from coming on--you may have that problem, too.

Have you cleaned the little magnetic sensors for the front wheels? All you need is an allen wrench to back the little bolt out. Once the bolt is out, gently wiggle the sensor back out of the hole. The clean it, slide it back in, and reinstall the bolt. You do not need to jack the car up, it is easy to do with the car on the ground--turn the steering wheel all the way in one direction, do the sensor that's easy to reach, then turn the wheel all the way to the other side and do the other sensor. There is an electrical connector for each sensor inside the engine compartment, on each inner fender. If cleaning the sensors themselves doesn't fix the issue, cleaning those connections would be my next move.

The rear sensor should not need cleaning (is is sealed inside the differential housing), but you should inspect the wiring for it. The rear sensor doubles as a speed sensor for the speedometer.

Good luck!

John