Finding the reason for clumped ice in an ice maker bucket is not always an easy thing. If you are lucky, the issue may be apparent otherwise you have to look for certain clues and use process of elimination.
This is how I would tackle your problem, it may not be elegant but it works for me.
First I would see if there is any obvious signs of problems like incomplete ice cubes, frost build up around the door or ice maker chute. This would give me a clue that the problem may be related to outside air. If not frost, as in your case, I may only do a cursory glance at the ice chute door, gasket and sealing capability of the freezer door. I do this on all fridge calls anyway. More than likely there is no air leak if I don't see frost. I then quickly see if the freezer door closes okay and engages the light switch.
Since I did not see any frost, my main focus would be on the ice maker and water valve. There is hopefully a perceptible leak so then I would start a harvest cycle with the ice maker. Most of the time If no frost is present, I start a harvest cycle even before I check the door, gaskets etc as mentioned in the previous paragraph since it's just a cursory check and I can complete it before the water valve engages. Btw with regards to your question about starting a harvest cycle ...no... only the whirpool style ice maker requires jumping. Your ice maker is started one of two ways depending on the type. If it has a white paddle, turn the ice maker off for about 10 seconds, turn it back on and press the paddle in three times within 6 seconds. If it has the metal bail arm, lower the arm and grab about two or three of the ejector "fingers" and gently but firmly pull then to you in a clockwise rotation. After a few seconds of doing this, release them and the harvest cycle will start. BTW the "fingers' as you call them on this style, are not in an up or 2:30 position like the whirlpool modular style when at rest. Remember this distinction as pulling the whirlpool style ejector fingers may destroy the ice maker.
After a few minutes, the ice maker will energize the valve. Water will enter the fill tube and run into the ice maker receiving cup. I'll look closely for leaking. If the tube or cup is partially frozen, water may fall in to the bucket. If so, problem found ..clear the ice buildup. If not, I'll look under and around the ice maker to check for any perceptible leaks. If a leak is found, I have to determine if it is coming from a crack or is the ice maker simply over flowing with water. If the latter, it may be possible to adjust the water fill level through an adjustment on the icemaker. This adjustment, however, usually adds or subtracts only about one or two tablespoons of water at the most. If this adjustment doesn't stop the overfill situation then I have to replace the valve.
If I still haven't found the problem then we have the dreaded (*&@#$!) imperceptible leak. That leak only shows up during lunar eclipses, on the 31st day of February or when you are not looking. It could be the ice maker unnecessarily energizing the valve or the valve itself. There's several ways to handle this. Replace them both or one at a time. This depends on how much time/customer's money you want to spend.
If the ice maker is more than five years old or has peeling Teflon coating, I would replace it first as it needs to be replaced anyway and see what happens. If leak continues after a few days, then it's time for a new valve.
If the ice maker is relatively new, I would replace the valve first since it is generally less expensive. If I get them from repair clinic I can always return the part that did not fix the problem.
There is also a neat test that can be done on the valve to see if it is the problem. Remove all ice and water from the ice maker, remount it but do not connect it. no...simply turning it off aint good enough. Keep it disconnected (or disconnect the ice maker side of the valve). If, after a few days, there is water in the ice maker, then undoubtedly we have a leaky water valve.
Other things to consider, ice maker mold heater not turning off, very high/low water pressure at the spigot, water filter issues and an out of sync ice maker, Whew! I need to start charging more for this repair. I'm exhausted just pretending to do it and I am certain I missed a thing or two. Anyhow, by now I should have solved the problem and it's time for a brewski. But no, can't since I'm pretending to be at work! All I can do is quietly celebrate by putting another victory notch on my screw gun.
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Source: GE refrigerator not dispensing ice