I was hoping not to touch the carburetor for quite a while but the engine cranks and doesn't start so we dug into it now. I know a little about carburetors but not enough and pulling one apart gave me a lot of insight. It still seems too complicated for what it actually does and this is supposed to be an extremely simple design!
Our Jeep has the same single barrel carb as any other original CJ2A - Carter W0 (or WO) model 636SA. It was used on multiple Willys models and a Studebaker. Rebuild kits are available from everywhere. I ordered one from Jeep1942.com because I liked the seller's personal touch and upfront product listing.
Luckily there is a spare CJ2A engine in my Uncle's shop (actually two). It's not worth much as it was under water at one point and the head is off. But it had a complete carb on it so I pulled it off and took it apart on the bench. That told us a lot. I used the rebuild kit on the spare while we continued working on the original carb. Rebuilding, cleaning, and re-assembling the spare carb gave me tremendous confidence in the mechanics of the carb but very little education on how it worked.