@SERampMike wrote:
How can I require this behavior without manually signing out of the app every time I want to shutdown or lock the desktop?
There is no such option, and even if there were, it wouldn't prevent access to the files already located in the local Dropbox folder.
If you have multiple people using the computer and you want to secure your Dropbox, give each person their own computer account. That will prevent them from accessing both the Dropbox application and the Dropbox folder.
