Hello Bondy,
The previous owner may have just missed something.
I have never worked on Greenfield wiring, but the principles should be similar.
If you have a seat switch, you must be sitting on the seat, to allow the engine to start.
If this wire is missing (blue wire), then 12 volts wont be applied to the coil of your start solenoid (white wire in your 3rd image), when you turn the ignition switch to the start position.
You can bridge out your seat switch, but it is a safety issue, as the engine wont cut out if you come of the seat for what ever reason.
The first test I would do, is to see if 12v is being applied to the coil of your start solenoid when the key is turned to the start position. (white wire)
You will need a dc volt meter or a 12v test lamp to do this.
If the result is zero volts, then you will have to fault find the seat switch wiring.
The aim is to ensure the wiring is continuous through the seat switch and then to the start coil
terminal.
Another test you can do to see if the starter motor is working, is to directly connect a 12v test lead to the solenoid start terminal.
To prevent any short circuit, connect a wire to the solenoid start terminal
first, then touch it to the positive terminal of your battery.