It is wrong to assume that the name Engine Stop solenoid is doing what it says.
I learned my mistaken understanding recently on a Kubota whose injection pump looked a lot like yours.
After I made the statement which turned out to be wrong, I studied the wiring diagram and to my surprise the solenoid actually enabled the engine to start when powered up.
Regardless of what it is doing, all these solenoids have two winding's inside. A pull in winding and a hold winding. The pull in is only powered briefly to move the hardware and then the hold coil takes over.
It is most unfortunate that Kioti does not make available parts diagrams and more. Every search I make says go back to your dealer. Kubota on the other hand has a wealth of on line info readily available.
The two wires going to your engine solenoid should have power present in one circuit when the key switch is on and on the second one also when cranking. The ground path is through the injection pump body.
This is the material regarding the Kubota.
I was wrong in stating the solenoids job is to stop the engine. Just the opposite
I have studied and marked up one model's starting system wiring.
The red line is 12 volts direct from the battery, through a fuse #6 to the open contacts in the engine stop relay. This is power waiting to be switched on at which point battery power flows through the blue marked circuit to to the left hand coil in the engine stop solenoid.
Turning the key to Acc, On, or start positions sends power through the yellow marked circuit through fuse #8. This circuit does two actions. It closes the relay contacts by powering the small coil in the relay and now battery direct 12 volts is going to the engine stop solenoid LH coil through the blue marked circuit. The second action is to provide 12 volt power from the key switch to the right hand coil in the engine stop solenoid.
Would you have as test light like this one?
I do not believe the voltage to the engine stop solenoid changes. The pull in power of the two coils in the solenoid itself is different but both coils see the same 12 nominal volts.
From memory, you do not find any sign of 12 volt power on either of the two wires to the engine stop solenoid. This means that either two fuses are blown, #6 and #8 or there is a problem in the key switch
Can you please give me more specifics about your tractor so I can study the correct wiring diagram.
This wsm material shows battery voltage sent to both solenoid circuits
This formal check of the relay may identify if there is a wiring problem. Squirrel chewed etc.
Dave