Basically you measure the resistance (ohms). If you have 0 its a broken wire, if infinate res, it's shorted out. Sounds like it has seperate coils, one for lights/battery (?), one for ignition. Wouldn't hurt to start checking wires/connections for corrosion, dirt, breakage/looseness. Be sure that any ground/earth is clean of any rust, etc.
You will need the correct flywheel puller for the flywheel to remove it. Anything else and you WILL be buying a flywheel too.