Well Kubota has two schemes for that solenoid so the answer is “it depends on what kind you have”.
One style of solenoid is not active during start and running, but only pulls the fuel flow to zero when the key is turned off, it holds fuel off for a few seconds and then releases to be able to run if working properly.
The other style has two coils and is active during startup and during running so the tractor will die when there is no power applied to the solenoid.
I believe you can remove the solenoid in either case and manually move the levers that the solenoid controls to make the tractor start, run and shut off.
I think if there are three wires to the solenoid it is the second type. If one or two wires then it is the first style. Some use the case as a ground path.
But search for some threads about how to troubleshoot the system and you will find some intelligent people that tell you how to do it.
See this for example
I bought a L3130/hst in 2005 new, which now has only 230 hrs on it. It has a engine block heater. I have no problem starting it, but as soon as i start moving (even after letting it run for a half hour) it sounds like a switch click and it shuts down. I makes the same switch sound as if i would...
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