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.
Starter relay john deere starter solenoid wiring.
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.
Topteng motorcycle starter relay solenoid oem starter relay fits for john deere lawn mowers miu12537 s240 x300 x304 x310 x320 x324 x360 miu12537 5 0 out of 5 stars 1 16 69 16.
Put up through tops stars team with september 9 2017.
Hope the picture helps.
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.
455 deere diagram.
This is an inline relay to the starter solenoid on the kubota black wire side.