The single cylinder Bridgestones use a magneto ignition and don't require a battery to run, but the ignition switch has to be in the on position. If you can't turn the ignition switch, you can bypass it by using a jumper wire from the black wire going to the coil from the ignition switch to the black wire coming from the magneto. There is a good 50 - 60 Sport Technical Manual downloadable from this site, but it doesn't have the color codes on the wiring diagram. However, if you also download the 50-175 Service Manual, the 50, 60, 90 wiring diagram in it does have the color codes. If you are able to turn the key on, the problem is likely to be dirty/rusty points similar to any old engine with points ignition.
