Depends on the switch you have.
If it has four terminals like mine, two will be for the start.. which you have apparently found (yellow/green and yellow/red at the back of the key barrel from memory, but don't ask me which is which unless I have a test light and I'm sitting in my foot well.) the other two are for the light... join one of them to the same ignition feed fromthe key barrel... and the other just join to the body somewhere.. negative earth...
I have my start switch set up exactly that way.. when you turn the key, the blue ring around the starter button lights up.. and by using the ignition wire from the key barrel to power the start button, you can't trigger the starter unless the key is set on ignition.
put it another way.. take the ignition wire from the key barrel.. (meaning it has power when the key is at ignition position.) branch into that wire and run two feeds (wires) from it.. one is to one side of the starter switch.. and the other is to feed power to the switch light. Then run the other light wire to body metal.. in my case I screwed it to one of the metal cable brackets under the column, then branch the other start wire to wire from the key barrel that has power when the key is held in the start position.
regards
Frank