If a county in which a turnpike authority under Chapter 366 operates or a county owning or operating a toll project under Chapter 284 is part of an authority, the turnpike authority or the county may submit to the commission a proposed structure for the board and a method of appointment to the board:
(1) at the creation of the authority if the county is a county that initially forms an authority;
(2) when a new county is added to the authority; and
(3) when the county is initially added to the authority.