The best I can see doing Jonathan is to add a dimension to the see empty pane sheet so that at least a user is not confused when everything is excluded. Though this makes the behavior consistent, it still may be a little jarring as both vizzes' panes appear and disappear with the filtering.
I have not yet been able to figure out a way to keep the pane on the see nothing sheet but I am going to keep playing with it a bit.
Thanks, Dan...have you had any other thoughts on this one?
I heard back from Tableau tech support, this behavior is by design.