My Steps 32 Series does the same as the OP video. Today I removed the motor and in my case it is not the gear that goes on the motor that is damaged but the big gear inside the gear assembly. Some teeth are shorter and the can not grab the motor gear anymore.
So I have ordered on amazon.ca Kwikee 1101425 Gear/Linkage A. This is the gear assembly for my 32 series. It is 96$Cad which is about 75$US shipping included.
First you disconnect the arm that goes to the steps, then you remove the motor (3 screw and a harness), then the gear assembly can be removed by removing 4 bolts.
I have changed my motor last year and I bought it also from amazon.
Fleetwood Pace Arrow vision 36.5 on Ford F53 1999 gas, V10, 6.8l with 4R100 Transmission