I have a Whirlpool sided-by-side refrigerator with ice & water in the
freezer door. Recently the water dispenser has started leaking. The problem
is definitely not that the dispenser switch is being pressed as I have
physically disconnected the switch for testing.

With the switch connected I press a glass into the dispense. The water
dispenses. I physically disconnect the electrical switch (that the glass
ultimately presses) but several drops of water continue to drip. Sometimes
it is just a few drops, other times it is enough to eventually overflow the
collector tray at the bottom of the dispenser. Always though it is just a
drip, a few drops at a time, not the full water volume as while filling a
glass.

Is this a common problem? What is the usual cause (a solenoid)?

If it is a solenoid (or other part) where is the most common place to locate
it (the door, freezer body, etc)?

Thanks