was struggling to find the TabRect function.
That's the way I found it:
CTRL+Left-Click on the identifier "TPageControl" in your source code, and the IDE will open the file in which TPageControl is implemented. If you landed in the implementation part of this unit, press SHIFT-CTRL+UP to get to the interface part. Now you can scroll through the declaration of all properties and methods. Don't forget what's inherited from ancestors: scroll up to "TPageControl = class(TCustomTabControl)", CTRL+Left-Click on the identifier of its ancestor, TCustomTabControl. Now you see what is defined in TCustomTabControl, etc.
Unlike any written documentation, this method is absolutely up-to-date. Of course, as application developer you cannot access anything which is not declared as public or published.