Nice! Welcome to the Eagle project world lol. The post on the bottom of the Auto solenoid is the ground. You can install a manual solenoid, which is cheaper, and just leave that wire hanging. It will work the same, but bypass the NSS. You can leave it like this permanently, or just do that to test it without spending as much. Either way, these solenoids are apparently pretty fickle. If you get one from Advance Auto, I'm sure you could take it right back after testing no questions.
You might also want to examine the fuel system, all lines leading up to it, and spray in some carb cleaner. The stock Carter BBD is known for having clogged jets.
Your AMC, since it has the 258, is highly compatible with many Jeep parts, so availability for most things mechanical should not be a problem. To save you some ID time, your model will generally have the AMC 4.2l 258 w/plastic valve cover, Carter BBD carburetor, Torqueflite 998 Transmission, NP129 Transfer Case, Dana 35 rear axle, and Dana 30 front axle. Common upgrades are Motorcraft 2150 carb, 4.0l cylinder head swap, and a high energy ignition, but you should probably solve the starting issues first. Not sure yet what other options there are for a starter, some other people around here might know.