I'd get a gauge on there to tell what you've got.
Yes, that's the shaft I'm referring to and yes you need to be operating to get balance between spring and fly weights to have control of the shaft rotation. The linkage in these governors is a bit tricky to change lateral motion of the governor into shaft rotation.
There is also a bypass valve and a check valve under the large cover. Have you checked their operation? Also check valves in the priming pump that were previously mentioned.
I'm now out of ideas. Let us know what you find.

One more idea...could suck air in around the priming pump shaft. Can't find a cross section detail of how it's sealed.

Right, time for an update!

After a bit of perseverence, I re-checked everything, put a fuel pressure gauge in the pump to check what was going on, put 10 gall in the diesel tank and with some renewed optimism we finally got the machine to breathe into life....after all that.....


But, and there's always a but, I have a minor problem with shutting the tractor off, setting the idle speed and max. RPM.
In one position on the splined shaft it will shut down OK, but only feels like its getting about 16/1800rpm, or moved on one tooth it will rev away nicely but can't shut it down without pulling the clevis pin and manually pushing the lever on the pump to "off"....I guess there are a set of initially measurements for all the rods and linkages between the lever and the pump.
The other perplexing thing is I can't get it to idle nicely.......I screwed the min engine speed screw right in but no reaction.....all i get is a gradual drop right back to some unhealthy very low rpms which can't be good....I assume something like 800rpm is where it wants to be.
Now when the customer bought the machine the mechanism behind this cover plate was full of water/sand dirt etc.....we haven't renewed it......I am guessing this is the box of tricks that will actually tune up engine speed settings, giving us a feel for 2000 > 800rpm and then "off"

Any suggestions?