When a member of a water resource board has a conflict of interest in a specific issue before the board or is unable to fulfill the duties of a board member because of physical or mental illness, the county commissioners may appoint a person to serve as an alternate to the disqualified board member. If the disqualification is for a conflict of interest, the alternate board member is to serve only for the purpose of deciding the particular issue causing the conflict. If the disqualification is for physical or mental illness, the alternate board member is to be appointed by the county commissioners only for one meeting at a time.