Electrical ??

Do you have voltages where you ought to have 'em, when you ought to have 'em? eg at starter solenoid, and does it click when you try to start?

What happens if you jump from the battery non-earth terminal to the starter terminal - does it turn the engine over then?

Even if you don't have a voltmeter, a length of wire and a bulb can be used to test the circuit for continuity/voltage.

That will at least show if your starter is working OK.

Your solenoid should click when you operate the starter mechanism - so if all is silent, I suspect you (or someone else) wired something incorrectly.

The solenoid should operate off a low current 12v (from the starter switch), and close a big pair of contacts able to carry the starter current. When this happens, the relay should click loudly.

You could try running a length of wire from the positive battery term to the solenoid to see if it works when you do that . . . . . but disconnect the starter first - at the solenoid end to prevent short circuits and 'Bangs'.

Slow methodical fault finding is the key, try one piece of the circuit at a time.

Right, now on to your question. This is probably the only valid test you can do on a solenoid - see if it clicks, but without seeing yours, I cannot give precise details - what you could try is as follows.

With one end of a length of wire connected to the positive battery terminal, flash the other end of the wire against the solenoid - on the connector that goes to the neutral switch - the solenoid should click.

From your description, the solenoid is wired as follows - the wire to the battery, and the wire to the starter (both big thick cables?) are the 'switched' wires. The body of the solenoid is grounded to earth and is the coil for the solenoid - and the wire to the neutral switch provides the momentary positive 12V to the coil, which pulls in the connector to operate your starter.

If it doesn't click, the solenoid is dead - replace it. If it does click, it looks like the problem is in the neutral switch - replace it.

I would not want to drive a tractor without a neutral switch - it is there as a safety feature, and should be respected as such.