I just joined as I am trying to resolve this same issue on an XR4040 for a member who just passed away last week.
Tractor was dead in the back yard for days but I got it running good again, but it just dies after about two seconds. Pull solenoid winding checks fine with an ohm meter. However, there is not a one amp fuse listed in the parts manual anywhere for his tractor, an XR4040 cab version with Hydrostatic transmission. It does list some 5 amp fuses and they are the smallest size I found listed in the parts manual.
The solenoid which screws into the end of the injector pump body has two sets of leads attached. One lead set is a pair which appears to open the solenoid and there is continuity there.
The second lead set consists of three wires and I have not been able to locate in the service manual any kind of test procedure for this set of wires or what it is inside that they attach to or their function. I read with interest the post which says there is an Start solenoid and a RUN Solenoid winding. However, I was not able to read any continuity through what may be the HOLD side of the solenoid regardless of which two wires within the three wire cluster I connected ohm meter to. Clearly, something is causing the fuel supply to the Injector pump to shut off. I need to insert the voltage meter and reverify whether voltage remains present to the PULL solenoid once key is returned to RUN position. In an earlier test I saw voltage still present going to the PULL side of solenoid but I only left the key in run position for about a second instead of for several seconds. I never found a single blown fuse nor did I find a single relay which did not close and pass current when energized from a separate external 12 volt power supply.
Any thoughts, suggestions, anyone? This tractor is about a two hour drive from where I live so next time I drive down to work on it, I hope to have a better idea of what I might be looking for, Owner was a best friend of over 25 years and passed shortly after his diagnosis of cancer before I could fully resolve tractor issue for him. I don't even know what user ID he used.
I actually worked briefly at an LS dealership but most of my limited tractor experience comes from repairing, rebuilding and maintaining personally owned farm tractors and machinery down through the years.