looks like you suffered the same problem as i had. The plastic housing for the rocker mechanism get weak over time and fails. I don't think there's any other solution besides replacement. My understanding is that the 360's, 400's, and 75/76 550 and 750's used this same handelbar switch, but if you replace it with another used one who knows how long it will last. My solution was to replace my handelbar switch with one from an earlier honda that has the simplified starter button. I had to do some detective work with hooking up the wires since it wasn't just plug-and-play but it works and now I have a manual on-off switch for the headlight.
My broken starter switch

What I replaced the handelbar switch with.

