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one other point I noticed and left off - my apologies.
The dispenser has a plastic sheet cover between the little motor (which looks like it is pushing a ratchet) and the door insulation. That plastic cover had a spot that looked melted, to the point where part of the sound insulation had stuck in the melted plastic.
That dispenser motor is also located close to where the sound appears to be coming from. The control board is upper right, the motor is more upper left, down just a touch.
Please see Item 8 on http://www.partselect.com/ModelFrames.aspx?ModelID=651675&ModelNum=GU1200XTLQ0&mfgModelNum=&ManufactureID=3&Selected=ACGOEJZI&Position=0&mfg=Whirlpool&Type=&Mark=1 , it is what I am using to identify the components in the door.
Thanks. I will replace that.