You need your idle-cut solenoid, if it is on a '77 2F-type carb. From what I observe, the magnetic charged pin is cutting the fuel-air-mix in a regulated way. There are multiple holes in the perforated tube that will attenuate the fuel-air mix thru this 'circuit.' Removing the solenoid as a whole part, leaves the passage unrestricted, free of the orifices that were designed in to it. The pin and perforated tube are integral.
From what I can tell, the bolt used was a M10 x 1, unlike the F-carb with two screws and a gasket, this one uses a conventional machine screw-thread with a copper crush washer (probably at the corner autostore, but thickness will change where that o-ring on the tip of the solenoid sits, I suppose I could measure one of mine). They sell solenoids, just by themselves for 2F. If you replace it, you will need to perform an idle-speed, and idle-mix adjustment.
IIRC, I used compressed air to blow thru the idle-mix screw hole, after I removed the idle-mix screw during a rebuild. I watched solvent move thru the passage, into the throttle bore, confirming its function. Because this circuit was exposed to PCV gasses, after ignition shut-down, it could be corroded? It could have varnish, or the threads on the delete-bolt could have flaked off galvanized plating. It is important to avoid oil dilution with gasoline, which could occur if the carburetor drewels post-shut-down due to the temperature in the engine compartment. 'Dieseling' is just a symptom, as I run a carb in a different rig that has no cut-off-solenoid.
The electrical circuit, for the solenoid, was in the original harness. On mine it runs on the 'Engine,' circuit and it shares a circuit with the voltage regulator.
Using the choke to keep it running is a bigger issue. I'd start by making sure that every spark plug isn't fouled with carbon or oil (because we know that it ran bad for at least a while). A weak spark will make it so the engine hold an idle a bit better with the idle-speed up, which occurs concurrently with the choke in a somewhat closed-position (pulled-out). Clean the spark plugs with a steel toothbrush, some 220 silicon-carbide, a worn-out small 'flat-head' screwdriver for a scrapper, and steelwool. I rinse them in solvent, or use compressed air. Folding the paper over on itself will fit in the gap between the electrode and grounding strap. Reinstall plugs with a minimal amount of dielectric grease where the rubber boot fits (keeps them from seizing). Then try to see if it runs without the choke.
