I believe your mystery wire, from guard switch goes to pin 12 of the rotary switch. However, when the guard switch is installed, which contacts are closed when the guard is in place? You need a normally closed contact there for this to work.
And your power switch #1 needs to be a momentary push button, normally open
For the moment, add that wire, then flip the power switch on then off, the motor should run until you move the guard switch, then it should stop. But you may have to hold the guard switch closed depending on how the lathe operates it mechanically
You also would need to add a stop button, (normally closed) in series with the same wire you are adding
You follow all that?