WOW! This is a beautiful clock, and that mechanism on the second hand... I'm amazed, the way the whole assembly turns, Ive never seen such a thing before! 10/10!
I'm not sure I understand why your building it the way you are.
Build the actual linkages, and make them function, then add little bits of geometry on top for looks and form. Just because there are lines there, doesn't mean it's a separate piece.