Tony
tc-sidebar-tabs-main should be in `$:/core`.
If you're convinced that making changes in ControlPanel/Sizes has no effect, then I'd have to suspect a corrupt class somewhere in that part of the dom. If you have a similar wiki, (or, indeed empty.html) load them both and bring up the DevTools Inspector looking at both sidebar tabs and check for difference between their respective styles.
I still think your solution will come from CP/Sizes. I know they can get thrown on rare occasions. If I walk through them (set to 0, then back to original) "something" kicks in and fixes the layout. Background to that: I use a couple wikis stretched across three monitors, so I have a very unconventional layout, and on the occasions when it goes awry, fiddling with those always fixes it - though in my case, it's the story river that explodes across the screen.