Why do you think it is in the gearing? My guess is that one of the pins that connect the shafts together sheared, that is what is giving you the clicking and no movement. There would be one between the motor and the gear reduction and one between the gear reduction and the first landing gear. You will have to get into the front compartment and get where you can see, then have someone work the switch and see what is rotating and what is not, then you will know what you have to take apart, if it is just the pin, line the holes and insert a new hardened pin.
03 Silverado cclb 3500 drw, D/A, Reese 22k hitch
07 Alfa SeeYa Gold 30RL,2 slides,power everything