Both conditions as you describe are correct, at least electrically. I have no clue as to how the carb solenoid works or under what conditions, other than power is only supplied when the key is in RUN.
+1, I have no idea how the solenoid is intended to operate ON THIS APPLICATION, but I can add this to the discussion. FIRST, a FORD produced Service Manual would be the best source of how the circuit was intended to function, a detailed wiring diagram would easiest answer every question, which I do not have for this year vehicle to reference. .
This above being said to next describe how I think the circuit was intended, based on the discussion so far.
In an effort to prevent "Dieseling", this solenoid is often added to drop the idle speed, effectively cutting off the fuel which prevents the dieseling (afterrun) of the engine. IT DOES NOT ALWAYS HAVE TO BE AN IDLE SPEED COMPENSATOR FOR AIR CONDITIONING as the O.P. seems to be describing. There are occasions, that people will call it such. AGAIN, refer to original wiring diagrams and if possible, assembly manuals for an exact account of the purpose this solenoid was designed to do and the correct method of making any connections. It seems Randy has helped sort some of the misconnections already but without a vehicle-specific wiring diagram, it would be difficult for any bystander to assist further...at least without pictures, such as Jeff is known for. Also, most of the time, the connections at the firewall are sprayed with a sealant at time of assembly, rendering a photograph only "some help" at best. Maybe somebody has a photograph of your exact optioned vehicle, but these years (1970) are ALL OVER THE PLACE when it comes to "exact list of options", making it rather daunting to be "correct" for your specific needs.