I worked on this generator
over and over again on a 424 I was delivering...
... had to troubleshoot 4 different failures in a 3 week time period.
Here is what I recall
from that experience.
I suspect the thermal time out issue is right, must be at least a partial flow of cooling
water, as the normal run time (from cold) to overheat is ~ 5-7 min... verified a couple times.
BTW, once you fix this, get an extra belt, AND an extra regulator
capacitor to put in your spares kit... Need not be a 'Phasor' branded cap, better to mount it outside the gen head
so as to avoid all the heat (that is what makes them fail).
Oh, and the 'self bleeding' feature may not always work as advertised (depending on your install). If not, just remove the return line from the injector and let the pump click over for about half a pint of fuel
... then the bubbles will come....