Whirpool ice maker overflow
It sounds like the water controll solenoid has something stuck in it allowing the water to flow. These solenoids are normally closed and require power to open. It is possible a small piece of pipe scale is holding the valve open. It is also possible that there is a failed component on the controll board but that is doubtful because it is running with the switch in the off position. With the unit unplugged and the water turned off dissembling the valve and cleaning it may clear up the problem but a new solenoid valve may be required.