Ctrl+Tab for toolbar tabs

We can cycle through the viewport tabs with Ctrl+(Shift)+Tab.
Which only makes real sense when a viewport is maximized.
In addition there are the viewport tabs.
I find myself using Ctrl+(Shift)+Tab very seldom.

But the toolbar tabs are click-only.
I’d find it handy to cycle through the toolbar tabs using Ctrl+(Shift)+Tab.
Like cycling with the mouse wheel.

Are there any means to get access to the tabs?
Then I could make a little script.