Update:
Today I decided to take the mechanism apart. Only the side which I could see the gear teeth. The other side says "Caution, Do Not Remove". I think it's because that's the side with the spring which winds up the belt. I could see that the sheet metal cover has a tab which holds the plastic cover on. See in the following picture.
So I started by removing the black plastic guide for the belt. It came off easily by putting a small screwdriver under the center and prying up. I had to hold the belt from recoiling back inside at the same time. See below.
Then I grabbed the shaft which the belts winds around with needle nose vise grips. There's a slot in the shaft, which I put the vise grips into. This stops the shaft from recoiling the belt and made it easier to work on. See below.
Then I used the small screwdriver to pry the sheet metal cover off. I pried next to the two tabs (left and right) at the bottom of the cover. The mechanism is upside down in the picture below. The sheet metal cover pops right off. Then you swing the cover up and off the housing.
Looking at the inside, I could see three places where the plastic cover goes into holes of the metal housing. It almost looks like a plastic screw, but it's not. I found out after getting the cover off that the slot allows the plastic to squeeze together and pop out of the hole. The slot in the plastic, in the hole, is shown below.
I carefully slid my small screwdriver between the plastic cover and the metal housing. I only had to push it in between. I didn't have to pry on the plastic. The screwdriver is very thin, and it wedged the plastic cover off the metal housing.
I had to repeat this in two more locations to get the cover off. I kept my hand around the housing and cover, and it's a good thing that I did. There's a spring under the cover, so you have to take the cover off slowly so you don't lose the spring. It's a light spring, so it's safe to take off. You just don't want to lose the spring.
I can't upload any more pictures, so I'll post and continue with another post.