The term of office of each member shall be three years with the terms of one-third of the members expiring every year. No member of the council who serves two consecutive three-year periods shall be eligible for reappointment during a one-year period following the expiration of his or her term. The Governor shall designate a chairperson and a vice-chairperson from the members of the council, to serve as such at the pleasure of the Governor. The chairperson shall be the chief executive officer of the council. All vacancies shall be filled for the balance of the unexpired term in the same manner as original appointments are made. The members of the council shall not receive any compensation for their services but shall be reimbursed for expenses incurred in the performance of their duties as provided in sections 81-1174 to 81-1177.