BB, the 30-seconds-then-quit outcome could just as easily have been a spark failure as a carburetion one, though after a very long period of disuse I would start with the carburetor. Unfortunately I tend to think of intermittent spark failure as more often a coil problem than a condenser one: I'm used to condensers causing hard starting and erratic running, or just no start at all and a very dull red spark if any. There does seem to be quite a possibility that you will be up for a replacement coil.
A long time ago I had a very elaborate machine on which you could mount coil, points and condenser, adjust dwell, and run the whole system up from idle speed to warp speed while observing the spark visually as well as with instruments. Unfortunately it was both heavy and bulky, and after not using it for 10 years, I dumped the whole thing on the nature strip. The surprising part was nobody grabbed it: I finished up putting it in a skip.
