I got hold of a service manual for my Jeep and took a look at the way the accelerator cable is supposed to connect to the throttle body. It turns out I was mistaken when I said that it looked like a single cable that was made in two pieces connected by a plastic do-hickie. Those were actually two separate cables.
Fixing the accelerator cable turned out to be as simple as snapping the end of it onto a small post. I’m so terribly glad that I was able to fix that myself rather than have my mechanic tow it in to fix it. That saved me $125 in tow charges.
-  Throttle Body. I laugh every time I hear that term. It sounds like a name that Charles Dickens might use: “Old Missus Throttlebody lived alone in the sprawling estate.” Hey, wasn’t that the name of the old lady in Great Expectations? ↩