Ford Repair: ABS engaging at slow speeds, dry pavement, air gap

Question
I have a follow up question about ABS but Jeff Wade is on vacation so I will post my original question and Jeff's answer followed by a new question:
Question:1999 Grand Marquis w/traction control.After replacing the right rear axle(brand new with proper sensor ring),bearing and seal after oil leakage the ABS system is engaging all the time at slower speeds and when comming to a stop.The ABS motor is "hammering" the brakes wich would be normal on icy roads but it does it on dry pavement but not at freewayspeed.So because the ABS sensor had gotten a lot of gear oil on it I replaced it with a new sensor.Everything is nice and clean and I also put on new rear brake pads & new parking brake shoes wich had gotten oily as well.The result is still the same and there is no warning light displayed.The warning light works because after getting tired of the constant brake hammering I disconnected one rear ABS sensor under the rear seat wich turns on the ABS light and traction control light and disables ABS altogether.I can't figure out what else to try,nothing else was changed except for the axle as described above.

Answer:Hi Stefan, It sounds like you might have the wrong axle or the ABS ring is dented or damaged. Also check and see if the number of teeth on the ring you replaced and the one on the other axle. They must be the same. Also check the gap between the sensor and the ring (called air gap)on on side and the one you replaced. That must be the same also. No dents or dings on any of the 4 ABS rings. Make sure all 4 ABS sensors are tight. If one ring has more teeth or the air gap is too big then the ABS system thinks that one wheel is moving faster than the other and sets the ABS system to operate. Thats the hammering you feel. It's the ABS pump motor working. If you need an easy way to disconnect the ABS system, just remove the ABS fuze from the box and put it back in to retest the system. GOOD LUCK!! (Jeff Wade)

I went back and pulled all 4 wheels and inspected the sensor rings and they have no damage at all.I also pulled out all ABS sensors and cleaned them thoroughly and they are in good shape.I also checked the air gap between the sensor rings and the sensor on all 4 wheels and it seems to be the same within one millimeter(this is NOT adjustable anyway).The number of teeth on the replaced axle's sensor ring seems exactly like the other side.The only difference is that the new axle's ring is shiny and that is because it was brand new.The problem remains the same-When I reach about 10mph I can hear that the ABS motor starts to engage and the behaviour is the same as descibed above.

Answer
even though you have no light and probably no codes stored you need a scan tool connected to this vehicle so you watch speed of each wheel-you won't receive a code if the computer thinks a wheel is locking up-you will only receive a code if the computer thinks there is a fault in the system like when you unplugged the sensor the computer seen an open circuit-with a scan tool you can watch each wheel while driving and at least you might be able to zone in on the wheel causing the problem-sounds like something is telling the computer one wheel is locking up and it that is the case the computer is doing what it is suppose to just got to find which wheel and go from there.-good luck.