In the event that a health care activity and an employees' bargaining unit shall reach an impasse, the matters in dispute shall be submitted to a board of arbitration composed of three arbitrators for final and binding resolution. The board shall be selected in the following manner: Within ten days, the employer shall appoint one arbitrator and the employees shall appoint one arbitrator. The two arbitrators so selected and named shall within ten days agree upon and select the name of a third arbitrator who shall act as chair. If, upon the expiration of the period allowed therefor the arbitrators are unable to agree on the selection of a third arbitrator, such arbitrator shall be appointed at the request of either party in accordance with RCW
7.04A.110, and that person shall act as chair of the arbitration board.