So, let's think about this...........The braces have to be in place above the headliner cardboard with the button pins installed and bent over, before installation can occur. You can't bend the tabs over with the headliner installed. So you can't install the buttons after the cardboard goes up.
So Tim's premise may be correct, in that the mini-bows and buttons are part of the 2nd piece of headliner and therefore it's components (buttons and mini-bows)don't have part numbers.