The term of office of each member is five years; provided, however, that of the members first appointed after August 1, 1995, three must be appointed for terms of two years, three for terms of three years, and three for terms of five years. If a vacancy to be filled occurs otherwise than by the expiration of the term of office of a member of the council, the appointment must be made for the balance of the term only. Other than the chairman, no member of the council who serves a full five-year term is eligible for reappointment during a one-year period following the expiration of the term. The governor shall designate a chairman and a vice chairman from the members of the council who shall serve at the pleasure of the governor. The chairman is the chief executive officer of the council. The members of the council may not receive any compensation for their services, but must be reimbursed for their travel expenses in the same manner and at the same rates as provided by law for other state officials for necessary travel in the performance of their duties as members of the council.