It might be the carb or a fuel pump. I suspect the problem is cheap to solve. This might have little or no rust.
“1955 Jeep CJ5. 4 cyl “F” head engine, manual transmission and 4 wheel drive. It is mechanically in good condition other than a current carburetor problem that allows it to start but not continue to run. It is currently in storage near Alva. but is priced F.O.B Oklahoma City. Asking $1500, or make offer. 405-833-7217″