The kill switch is hooked up correctly and should function OK.No sign on diagram of what you did with white wire,did you hook it up per my instructions?.It looks to me that you have one bulb for "high",the center position,one for "low ,the left position,and the right one is the "off" position.If these bulbs are identical it doesn't make sense that the engine would quit.Are bulbs identical ?.Is it possible that in the left pos. both bulbs are connected?.That would kill the engine.Have you used this light before and are sure it's OK.Further tests:Take out the low beam bulb, run engine and put switch in center position,high beam light should be on and engine should keep running.Repeat with other bulb, should do the same. Now switch to left position.Does engine keep running? if not, there is a short to ground at the switch or at the bulb.If engine runs and high beam bulb remains "on", the switch turns both bulbs "on" in the left position! That's why engine quits, too much of a load
Next test: move bulb from high beam position to low beam position.Switch to center position bulb should not light.Switch to left pos. and try again, bulb should light and engine should keep running.This pretty much checks things out.