The engine is a tank-under-carburetor type, so the fuel pump consists of a rubberised diaphragm sandwiched between the bottom of the carburetor and the top of the fuel tank. Being rubberised cloth, it is not unusual for them to give trouble when they get old (like 28 years old, for instance). I suggest you follow my previous suggestion of trickling a little fuel into the carburetor air intake with the engine running, and see if it keeps running. If it does, the diaphragm and the carburetor internal passages need to be checked. If the engine stops anyway, even when you do the fuel-trickling thing, you may have an ignition fault. Incidentally the engine's top sticker says that it has Magnetron (i.e. no breaker points) ignition, which was introduced in 1982. This means you have no reason to remove the flywheel at present.
