The yellow/red wire on the solenoid passes thru an eight wire "gang connector", and also a single wire connection in the headlight shell on its way to the starter button. The button grounds the solinoid when pressed, operating the starter. Check for a disconnected or dirty connection for that circuit inside the headlight shell AND the 8 wire connector. The connectors tend to corrode from dirt and moisture. Could be broken wire, defective solenoid, starter button, or button not grounding as well.
edit Might be another single connector in yellow/red wire just off solenoid. Check it too.