Way cool.
Your bystarter is AC voltage supplied. It has a pair of opposing diodes, and a resistor to reduce the voltage from 250Vac to 12v ac/dc.
What we're (you're) gonna do is eliminate all that slop/extra components, and go direct for 12Vdc.
You're gonna have to pick up a new +12V that is key switched. ANY +12 will do. Maybe the seat light? maybe the blinker power BEFORE the switch? Any 12V that turns on w/ the key.
The yellow wire from the bystarter goes to that +12, and the green wire will go to ANY easy to get ground. Add a ring terminal, and double it up on the starter motor? Maybe one of the green wires to the lights... Any ground.
My guess is the resistor or one of the diodes failed. It's not hard to sort that out but it is a weak link, and will fail again.
I'm glad you double checked. Oh yeah... The idle mix will compensate for either choke or no choke but not both. The choke adds a LOT of extra fuel. More than the pilot jet can pass on its own.