The little nylon button is a tight press fit in the genuine Lucas points, though they are often missing. It can be quite a struggle to get one back in place, they are not designed to be removed, the recess in the moving contact is larger at the bottom than at the top for the button, so they cannot be reversed for use in a clockwise assembly.
I dont think they are, or ever were, available as a spare. All the small bits for the points assemblies seemed to be supplied together in what was described as a magneto "Sundries" kit, but having had a few of these "Sundries" they did not include the button.
The repro points with the black button have recesses the same size and the btton is not a toght fit, allowing it to be used for either anticlockwise or clockwise assemblies.
If you can find new old stock Lucas at a reasonable price they are worth buying.