Thanks Derek and Marc, it does help.
After some more experimentation I have found that if you draw a rectangle by hand (with the pen tool) then you can select the points if the path layer is selected but if you use the rectangle tool then it must stay a rectangle. I can’t find a way to select the points of a rectangle.
It’s the first serious AE idiosyncrasy I’ve found 😉
Whilst I’m posting, Ctrl+tilde(accent grave) doesn’t minimize the ‘control lanes’ or whatever their official name is. Any ideas? It’s the top left key on a UK keyboard layout right?