This is probably your issue, there is an update to replace some parts, inside the governor, to an updated design, to eliminate the little tiny clip that fails and causes a "No Start" complaint.

A big city, type of CAT dealer (read this: as a big main CAT dealership, with all the special tooling and test machines, In Their Shop), should be able to "go thru" and update your 3116 "9GK" governor, then run on a special test machine (to verify).

{ Note: The updated parts are a little confusing to install, and I think they "can be" stacked and/or assembled incorrectly, during reassembly. My old dealership just had one mechanic on Dayshift, and one mechanic on night-shift do ALL those 3116 updates, to eliminate those types of assembly failures; Plus those 2 guys got fast and efficient at that update = they got 3116 governors mailed to them from 2 other states, also. Hawaii and Alaska}

Yes, that sleeve (once clip is removed) just slides towards the inside of the cylinder head. Those sleeves can be stubborn. CAT shows using rubber jaw'd pliers, but they have only slipped on the stubborn ones, then I had to use metal channel locks, just to get stubborn sleeve to "first rotate", then the next set was to get slide back. (Note: if the sleeve has every been slide, once before, and previous mechanic lubed the O-ring, then it will be really easy to move. The problem is when people or the factory assembled it without any lube, then they are stubborn)

The sleeve won't touch anything going into the cyl. head.{once sleeve is slid, then you will see E-clip and pin that attaches governor link to rack link} We always install a new E-clip.

Valve cover should be pulled if you install a reman , anyways to set the F.L. spec, with dial indicator and CAT tooling (otherwise you are just guessing that the new reman governor unit is adjusted correctly to the rack and its injectors)

Also, we also ran reman governors, on the CAT governor test stand, to unsure the settings were correct for that HP and serial number of engine; then they got installed on a engine (many years ago, we found too many not adjusted correctly, BUT then CAT reman got better and they started testing correctly "out-of-the-box")