I made a quick "jumper" cable (having bags full of crimp-on connectors is incredibly handy) to run between the terminals inside the connector and those on the oil pressure sender to ensure a good connection - fired the car up and right away, the oil light has gone away, and within a few minutes, the choke was totally open and the car was back to its normal self - and not smoking or trying to burn my eyes and nose with nearly-raw gasoline.
The old choke probably wasn't busted - but, I have a new one on there now, and the factory connector, so that is worth it to me (and I have the old one, just in case).
Now I just need to solve the other issue of that funky idle that'll hop up high (it was idling up to 2500 at first - really have to give it some hard revs to drop down to where it should sit. It's almost like a light switch when it changes to start running higher.