The Governor shall designate one of the members so appointed as Chairman of the Board. The Board may elect one of its members as Vice-Chairman; in the absence of the Chairman, he shall have the same duties as are conferred upon the Chairman. The Chairman shall be a full-time state employee. The Governor may designate no more than two other members of the Board as full-time state employees. Members of the Board not designated full-time state employees shall be considered part-time state employees.