The board shall consist of five members, four of whom shall be appointed by the chief executive officer of the county, city, town, fire district, or other governmental unit involved, and shall be qualified voters of the county, city, town, fire district, or other governmental unit involved. Two of these appointments shall be made from a list of four or more, submitted by the employees. If the request for arbitration is initiated by petition of the employees, the petition shall be accompanied by a list of four or more persons. If the request for arbitration is initiated by the county commission, council, board or other governing body having direction and control over the fire department, the chief executive officer of the county, city, town, fire district, or other governmental unit shall mail a copy of the resolution, together with a request for the submission of a list of four or more prospective members of the firemen’s arbitration board to representatives of the employees of the fire department. The four members appointed by the chief executive officer shall select the fifth member of the board, who may or may not be a registered voter of the county, city, town, fire district, or other governmental unit involved. The board shall meet and organize as soon as possible after its appointment. The board shall select from its membership a chairman and any other officers it considers necessary, and make rules of procedure governing its hearings.