As suggested by the InputEvent Documentation, I want to use _UnhandledInput to handle inputs when they are not already handled by the GUI.
My Scene looks like this
EditorWorld node implements
_UnhandledInput (and calls
SetProcessUnhandledInput) but the method is never called even when I don't click on a visible control.
_UnhandledInput on other nodes in the tree does not produce any results either.
I set the mouse filter property of all the transparent controls to both
Ignore but the result is the same. The events are all stopped by the UI layer and never fire the
_UnhandledInput method on the rest of the nodes.
Here's a view of the UI scene in the Godot editor. I have added the orange rectangles to show the invisible spacers.