Replaced the ice maker which behaved the same as the one I replaced. On advice from Appliance Parts Pros (cannot say enough good things about these people) replaced the main computer board. It fixed the problem. It also turned out the original ice maker was never working properly. Instead of cubes, the original ice maker dispersed broke pieces which not only went into your cup but all over the kitchen floor. The new unit makes perfect ice cubes now.
Unplug fridge from wall socket. Ignore the caution "ONLY TECHNICIAN SHOULD REMOVE". Remove the two screws on the metal panel in the back of the fridge. Remove the metal panel. Unplug the wire harnesses on the old board. Remove the old board. Install the new board. Connect wire harnesses. Replace panel. Plug fridge into wall socket.