I have not had an Autocord that I needed to repair the winding gears, but I do clean the gears underneath.
Tools: dental chisel, pointy tweezers, and slotted screw driver.
You will note that my Autocord is missing the knob on the winding arm. I used my parts camera to replace it.
Unscrew the strap lug and the back door hinge.
Use pointy tweezers to unscrew (anticlockwise) the locking screw for the winding arm (note that there is a washer underneath it) and the winding reversal button.
You will need to remove the leatherette covering from this side to reveal the five screws. This will take you some time if you want to remove all of it, so you can just work on the areas around the screws and come back to it later.
Remove the five screws and pull off the cover plate.
Note the bottom will lift up as there is a spring underneath.
The indicated area is where you will find the winding shaft spring, set plate and gear.
You can clean off the gears with Ronsonol.
Before you put the cover plate back on, clean the backside of the windows and add a dab of Super Lube around the center wind post.