cool post, nice to see someone ask why.
why does it start and run. that's because the ignition and lighting coils are separate.
whats up with that ignition switch. its antique balanced force regulation bullshit.
now Ill say how to fix. method 1. run it stock. find the lighting coil. there will be 2 wires coming out of the lighting coil. the bright one goes to the headlight and the dimmer one goes to the tail. use your manual.
method 2. rewire to modern. find the find the lighting coil. there will be 2 wires coming out of the lighting coil. the bright one goes to all the lights on the bike and the dimmer one gets n/c. (remember the other side of the headlight lighting coil is grounded. that means you need a half wave 12v rec/reg.) the fix will need leds because its half wave. so its headlight wire to the r/r to led's. run the horn through the r/r. battery or big cap is your choice.