Your copper contacts inside the main drive wheel are probably black. If you can remove it without breaking it and cleaning it then that might fix it. Probes rub against that copper and power up the heater or kill the heater after the fingers travel a short distance. The motor is not strong enough to move the ice till it melts. Wiggling it makes the heater contacts power up the ice mold heater. Might just need a new ice maker. Click pix to enlarge: