Congrats, its neat when you can fix something yourself and save 40 bucks. Yep often on solenoids or mechanical push start switches the contact washer or contact end posts themselves get burned and pitted and carboned up which wire brushing and/or filing smooth and/or turning over or around will cure.
I agree that looks similar to what I call Ford type solenoids but with ONLY the small S activation coil terminal. The Fords had 2 small terminals S for Solenoid activation and I for ignition which was hot ONLY while cranking which could by pass a ballast resistor. Of course that could still be used on a tractor that didnt have any ballast or by pass by ignoring that I terminal.