The drive motor is only going to running for very few seconds, just long enought to move the cams to the next spot on the wheel.
If the drive motor is bad , the unit will not switch tanks nor will it move the upper piston to the different spots for the cleaning cycle.
When the float is down the air should be able to go either way, if it is up the air should not be able to go down.
There was awhile back a float assembly that had a rubber washer go bad it is at the base of the float arm.. where it goes into the body of the assembly. if that rubber went bad, then it could not draw water out of the brine tank, but it could and would let water in to the brine tank.
If I am losing you on this and you need the phone... pm me and I can send it to you.. no cost...