This part shall take effect when:
(1) Three (3) or more of the counties of Dickson, Hickman, Lewis, Perry and Wayne and the cities of Dickson, Centerville, Hohenwald, Linden and Waynesboro are authorized by a vote of two-thirds (2/3) of their respective governing bodies to become members of the authority;
(2) Evidence of such authorization is proclaimed and countersigned by the presiding officer of each ratifying county and city and certified by that officer to the secretary of state; and
(3) The governing bodies of all governments voting to become members of the authority have indicated their willingness to appropriate sufficient funds to provide for the initial administration of the authority.