If what I throw out here, doesnt look like what you have.
Then it's best to let someone else step in.
Is that just twist it to start, then release it and it springs/rotates to the run position, type of switch?
IF so, it should be a common item somewhere.
I'd bet that a NAPA or some parts store has something you can use.
Brand probably isn't too important.
Just make sure it's built heavy enough for the load it will switch.
Extra keys should be cut on your way home from the store!
(then you can do like me and forget where i put 'em)
http://www.boatfix.com/how/SwDiagM.jpg
I'm thinking of something with 3 terminals, like yours in the picture.
"B" this terminal connects to the accessory lead on the battery.
"S" this terminal goes to the starter solenoid.
"I" goes to the ignition.
Forgive me if you already know all of what I pecked out.
just hoping to give a decent starting point for figuring things out.