Hi there,
the start will only work if the brake light is powered , but first i have a question , when you use the left brake is there no brake light or is it flashing when pul it on and off ?
Ihad the same thing and i have replaced the switch for new ones not so expensive and no more surprises.
if you want to know the part number just give a reply with type and year.
greetings
Hans van der Meijden
Netherlands