The water supply for our icemaker does not shut off after the ice tray has filled. I suspect I either need to replace the control module (Whirlpool AP4359694) or the inlet valve kit (Whirlpool AP3085178). Is there any way to definitively tell which part is defective?

More details:
When the ice maker starts to overflow, I can move the sensor arm into the "off" position, and this stops the water flow. I can then move the arm back down to the "on" position, and the water flow does not resume. After the water freezes, the maker will expell the ice, then the water fill cycle will begin and eventually overflow. Again I can move the sensor arm into the "off" position and this stops the water. I seem to be able to repeat this indefinitely.

Thank you for your help.