How do I lengthen the timeout period beyond 30 minutes?

Go to System Settings->Privacy & Security, click "Advanced..." at the bottom. Either turn off "Log out automatically after..." (as in the picture below), or set the time you want.

If it doesn’t offer any other times in the GUI in Settings, it may be possible to edit the plist file, but I’m not sure where that is stored.

You can just turn it off, thus extending it forever.

What timeout period?