The solenoid is just a big current electrical switch. So a smallish current can make the solenoid make contact and pass a very high current to the starter motor. This gets around having to have a massive switch instead of the wee one on the start/ignition cranking switch.
Usually the battery negative is directly grounded to the chassis somewhere near the battery, then a heavy cable/wire is taken to the solenoid. All that is needed then is to get that solenoid to switch and the starter circuit is energised- the motor turns - the engine starts. A relay, contactor, start solenoid are all the same family. They have a low current circuit switch a high current circuit.
Remove the wire that feeds the solenoid and see if there is continuity with an ohmmeter. It will be a very small resistance if working. One terminal of the meter to ground/chassis, body of solenoid/motor and the other terminal to the hot contact of the solenoid.
If you do get a low reading connect a wire from the battery positive to the hot terminal on the solenoid to see if it clunks on off. You will need a good connection to the body of the solenoid/motor or chassis. If the battery is still connected on the tractor this will do fine. I would remove the battery positive while you test.
Be careful to remove the wire that goes to the starter as you don't want the tractor moving off on you. Or put in neutral- just think it out.