Ice dispenser is cycling--on for a minute or so, and off for a minute or so--and pressing actuator does not affect this. So it seems a good guess that this switch is involved. How difficult is it to gain access to these parts to check?
Answer Ben, Here's the basic information you need to access the switches and wiring for the dispenser. "Disassemble Ice ‘n’ WaterTM Cavity
1. Apply masking tape to blade of putty knife or screwdriver. Use masked tool to remove plastic Crush/Cube selector button from dispenser-cavity escutcheon.
2. Use masked tool to pry bottom edge of escutcheon up, away from door. Pull remaining three sides of escutcheon up, away from door and set escutcheon aside. 3. Remove two screws that anchor electrical bracket cover. Separate cover and bracket to access ice,
water and cavity-light switches. 4. Remove two screws and clips that anchor water actuator arm and return spring. NOTE: In reassembly, return spring straddles arm and rides up against top section of arm. 5. If you want to replace the water tube, remove watertube retainer clip. Pull water tube out of door and thread new tube through. 6. Remove four screws and clips from ice door. Remove ice door delay-retainer screw and retainer. Remove ice door and delay mechanism. This is a "mechanical" system and has no circuit boards, so you'll be looking for loose wires and switch plungers etc. Thanks and Good Luck