Bumping a very old post.
I have the same problem - dry whirring sound that persists when the car is off. I tried disconnecting the battery for a few days, and the sound returned when I hooked the battery back up. I pulled the fuse for ABS and the sound stopped.
Before I pulled the fuse, I checked the ECU with my datalogger and saw no fault codes, but I have since found out that the ABS controller is separate from the ECU and so that's to be expected. My question is whether I can be sure that the problem is the ABS pump, or if it might be the ABS controller instead? Just trying to narrow it down before I start buying replacement parts.
On a related note, anyone have the part numbers for the ABS pump (and/or controller) on a '95 Spyder VR4?