Well I'd say you found the problem.
We usually replace whole motor so I've never tried to find just the switch.
You might try using manufacturer data on the motor to look for parts or see if there's a local elec motor repair shop near you and get lucky, I doubt GE made it as the same brown switch is on most motors I've seen.
You'd need to cut that overheated and corroded wiring back to a good spot and crimp new terminals on or you'll be doing it again soon.
You may find a used appliance shop nearby with a boneyard that might have something too.