When nothing is hovered, the root node remains selected, leaving the "Build Engineer Overlay" showing.
Click-to-open doesn't really help when it leaves a tooltip with nothing hovered anyway.

This is doubly troublesome given that the tooltip shows behind the windows for other mods such as MechJeb, TCA, and Blizzy's toolbar. This appears to have some support for not occurring with Stock UI elements, so maybe integration with clickthrough blocker or similar might solve it?

Additionally, clicking the hotkey when "Click to Open" is enabled should show the big tooltip even if "Visible" is set to false, as well as if "Names Only" is enabled.