electromagnetism - How do electrons know when a circuit is closed?

I was told that electrons do not begin flowing unless the circuit is closed. The electrons from the battery are not in the ends of wire when it is open, apparently, as there is no reason for them to go there. They do not "test the waters", so to speak. So how do they "know" when the circuit is closed?

Also, when do they know? Do they know the instant it is closed? Please resolve this vexing problem for me.