To disassemble the solenoid you have to desolder the contacts and then resolder them when you put it back together. I did the disassembly, looked at the insides, and decided to buy a new one. It's about $50, it's mission-critical, there didn't seem to be any pieces on the inside to replace and I didn't see anything I could do to make it better. Sure, I probably could have taken it apart, cleaned and lubed it and put it together, and it would have worked for a while. But I've learned you rarely get a durable repair that way.
Although I will say these Chinese tractors do seem to have a lot of pieces where taking it apart, cleaning and reassembling it does fix something.