We tried to see if we could get the ignition to create a spark. We removed the battery that was clearly bad and attached a trickle charger directly to the bike. Bad idea? I don't know. Anyhow, it seemed to work, but neither plug was producing a spark.
We removed a bunch of components in order to simplify our problem(s). We removed the gas tank, seat, chain guard, shift lever, clutch linkage housing / front sprocket cover, oil container, batter tray, tool tray.
We decided to learn more about points / condenser ignition systems before proceeding.
We made some adjustments and were able to get a spark. We feel that the condensers are likely bad as there is a spark between the points when they open. We plan to replace the condensers and the points.
We next decided to disassemble the carburetors. The throttle cable for the left carburetor was broken and pulled right out of the carb. The left carb was severely fouled on the inside with a white powdery substance. It would not have operated in such condition.
We decided to soak the left carburetor in gasoline to remove the fouling, and to try obtaining rebuild kits for the carburetors before reassembling them. We also need to get a new throttle cable to go between the junction and the carburetor.
Thanks to Tobin and Louis for your help.
Schucks did not have a replacement battery for us.
We bought some 2-stroke oil (valvoline, synthetic).
We looked for books at a number of stores. Bought one describing 2-stroke engine tuning.
Today we reassembled the carburetors (sans new gasket kits). The left carburetor was heavily pitted, but no holes so it should be ok. There are a number of good pics of the carburetors in various states.
We couldn't find a replacement throttle cable to attach to the left carburetor, so we "fixed" the existing one by using solder on the end of the cable instead of the factory "nubbin" that anchors the cable. So far so good.
We started the bike tonight! At first it ran only on the left cylinder, then it quit firing and only the right cylinder fired. We suspected at the time that it was because of a broken piece inside the left carburetor that emptied the bowl and tricked the carb into not refilling it.
Tonight we fixed the headlight wiring and reattached the headlight assembly. Works fine.
We "fixed" the clutch cable, though a replacement would be good. We discovered that adjusting a newly installed clutch cable is, erm, interesting.
We started the bike again and, like before, it was only firing on the right cylinder. We removed the left carburetor and discovered that the bowl was full of fuel, ruling out our prior hypothesis. We checked the fuel mixture against the other carburetor's setting, and discovered that it was set WAY too lean.
After resetting the fuel mixture we started the bike and it seems to have fixed that problem, as both cylinders fire now. The ignition and fuel mixture are in dire need of tuning.
We took turns riding the bike around the block to a gas station so we
could air up the tires that were pretty much flat.