If after a reasonable period of time, the Governor and the recognized employee organization fail to reach agreement, the Governor and the recognized employee organization may agree upon the appointment of a mediator mutually agreeable to the parties, or either party may request the board to appoint a mediator. When both parties mutually agree upon a mediator, costs of mediation shall be divided one-half to the state and one-half to the recognized employee organization. If the board appoints the mediator, the costs of mediation shall be paid by the board.