These things often use a crimped connection, and if someone got sloppy and didn't strip the wire first (most crimps require this, but not all), then you may have a high resistance connection. If it is 110 on the input and 100 on the output, that would be my first thought. If you take a small pin, you can pierce the insulation (be very careful and do it with the power off!), then measure the voltage after the connection. An alternative would be to cut it, then repair it with a wire nut. So, since the water switch seems to work, it sounds like it is the supply end of the connector going to the ice maker solenoid.