The members of the Commission shall serve without compensation. The Commission shall select its own chairman and determine its own rules of procedure. Vacancies in the Commission shall be filled for the unexpired term in the manner provided for making the original nomination and appointment, provided, further, that the employee group shall have a period of thirty days after notice that such vacancy has occurred to appoint the person to fill any vacancy occurring in the positions held by their nominees. If the employee group fails to so nominate a person within said thirty days after notice by the Clerk of such vacancy, the Mayor shall forthwith appoint, subject to the approval of the Council, such member without regard to such nomination procedure.