So, no spark. For now, disregard my fuel question, but still interested in how long it's been since the engine ran. What size engine (hp) is it? There are different ignition setups based on what size engine you're dealing with. I would assume 10hp or less based on the fact that you indicate it's a two cylinder. If it's small, I agree with Rich. Your problem is likely under the flywheel. Coils can even go bad on an engine that old, but as Rich said, start with points and condensers (if applicable).
You mention changing the cutoff switch. Are you sure that the cutoff is wired correctly and in the RUN position? Common ignition related problem that will drive you crazy.
Are you seeing much corrosion at wiring connections, crimp-ons, etc?
If there are coils under the flywheel, often the plug wire was stabbed into a recess in the coil with a pointed connection that stuck into the plug wire core. This connection should be checked for burn/corrosion also.
Corroded connections, broken wire, shorted wire, burned points, condenser, cracked/swollen coils are all things I would look for when you get the flywheel off.