Doesn't your ignition switch have three positions? My '82 MJ50J Towny has 3 positions: (1) OFF (2) START (3) RUN. For safety reasons you are to switch the key to position (2) START while off the bike. Then, while still off the bike, start the engine. While holding the rear brake lever (left hand) bump it off the centerstand then seat yourself in the saddle. Now you may switch the key to position (3) RUN.
When you unplug that electrical connector in the headlight shell you defeat the ignition governor and you should be able to start the bike even without the key. Here are some pictures from my owner's manual: