I didn’t have YouTube when I was a kid back in the ‘60s… so I had to get infamous in other ways… LOL…. but, It’s always gratifying to find You Tube has plenty of adventurists online… A simple “Google” of “How to repair a starter solenoid” gives several examples:
UNdoubtedly, the Kubota solenoid has similarities… for example, the plunger likely actuates a sliding gear-engagement mechanism.. But if you carefully inspect as you disassemble you will be enabled to diagnose and devise a repair. (I don’t care for his “aluminum ring” in lieu of the “E”-clip, which I would have preferred…but …Hey! Each to his own!) The most likely problem is the contacts….and unless the solenoid has been overheated from excessively long starter operation without cooling-off periods… you may not have to re-wind the coil at all.
Good luck!…. and come back, post pics, and show us how you get along!