Why not give the user running the EN application whether to actually log out or not? Under "Option" -> "General", you could add a checkbox saying "Automatically log out the current user when exiting Evernote". When the user closes the Evernote window, EN can look at that checkbox. If it's checked, perform the operation File -> Sign out User then File -> Exit. If not, the just File -> Exit. It isn't that hard unless I'm missing something.