Greetings Jason,
Here is the sequence of operation of the ice harvester after it has been filled with water from the solenoid valve at the bottom rear of the refer. The built in thermostat inside the harvester determines it has ice inside the tray. When that happens it does the following: Turns on the tray heater and starts the harvester fingers in motion, by the time the fingers reach the top of the ice cubes, the heater should have loosened them in the tray. Just as the fingers have finished pushing the ice out of the tray, you should hear the water solenoid engage and see the water refill the tray.
Usually water dripping down and freezing on the back wall is an issue with the solenoid valve not closing all the way and overfilling the tray.
RV refers do not harvest like a residential refer, usually takes 6 hours between harvests under ideal conditions.
Hope this helps, Blessings, Fred