Can I force logout after at time while still open?

[RogerTheShrubber]

I'm needing to configure a Roundcube install to be fairly restrictive and as secure as possible. I have found the "session_lifetime" setting and set it fairly low, but it seems that if a window is left open it doesn't log the user out. If I close the window and return after a few then it requires a login again, which is good. But I'd like it to log out (or at least prompt the user to stay logged in) if the window is left open. Any way to accomplish this?