(a)   Except for the initial terms of office hereinbefore specified, the mayor and the members of the Board of Commissioners shall serve for terms of four years beginning the day and hour of the organizational meeting following their election, said meeting to be held as provided in G.S. 160A-68; provided, they shall serve until their successors are elected and qualify.
   (b)   No person shall be eligible to be a candidate or be elected as mayor or as a member of the Board of Commissioners, or to serve in such capacity, unless he is a resident and a qualified voter of the Town.
   (c)   If any elected mayor or commissioner shall refuse to qualify, or if there shall be any vacancy in the office of mayor or commissioner after election and qualification, the remaining members of the Board shall by majority vote appoint some qualified person to serve for the unexpired term. Any mayor or commissioner so appointed shall have the same authority and powers as if regularly elected.