I would like to suggest the idea that when you double-click on an empty area of the taskbar, it will launch a new default lister. Same as 2x on the desktop.
I suspect there's no way to do this. Double-click on the desktop works because Microsoft have an API (and miraculously enough, it still works after all these years) to query whether there is an icon underneath the mouse cursor or not. There's no such API that I know of for the taskbar, so we would have no way to know whether where you double-clicked was actually empty or not.
The author of 7+ Taskbar Tweaker seems to have found a way to handle these clicks. He offers some tech info as well.
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II tried it once using a 7tt but it turned out to be too hard.