The Board of Zoning and Building Appeals shall consist of five (5) members, made up of two (2) Council members and three (3) residents appointed by Council, beginning no later than the first regular January meeting of Council. Resident members shall serve for a term of four (4) years. A member of the Planning and Zoning Commission shall not be a member of this board. A vacancy occurring during the term of any member of the Board shall be filled for the unexpired term in the manner authorized for an original appointment.