There shall be a Board of Zoning Appeals consisting of five (5) electors of the City appointed by Council to serve for a term of four (4) years. Of those first appointed under this Charter, two (2) shall serve two (2) years and three (3) shall serve four (4) years. The Board shall establish its own rules of procedure, keep a record of its proceedings in all matters coming before the Board. No resolution overruling an action under the Zoning Ordinance by any administrative officer of the City shall be adopted except by the affirmative vote of four (4) members of this Board. Council shall fill all vacancies by appointment for the unexpired term.