I have checked the outlet to make sure there is power and reseated the plug of the water softener, and still this evening it is running.
There is water coming out of a drain pipe that goes to a floor drain in the laundry room. When I turn the dial, I can hear that something has changed (sound of whishing water changes) but It just won't actually stop.
It is a "double tank" and on the side of the little tank it just says "Automatic Water Softener".
I think the make is Culligan, and the model may be for just the controller part, but is A-167-0, A-364-0, D167-0.
See the picture below.
Thanks,
Ash