Just follow the wires on the relay.
Starter relay john deere starter solenoid wiring.
455 deere diagram.
One way to test the solenoid and starter use a jumper wire from positive side of the batter to the small terminal on the solenoid.
The other relay 1 black and 1 red wires are just getting power and ground connections so it can connect the complete circuit to the starter solenoid.
This is an inline relay to the starter solenoid on the kubota black wire side.
That is all it is.
If the engine cranks then the solenoid is not the problem rather key switch and possibly as safety switch or short open or some such in the wiring.
This specific photograph john deere 316 solenoid wiring diagram john deere 318 starter intended for john deere 455 wiring diagram over is usually classed along with.
Hope the picture helps.