When a vacancy occurs in the office of an elected county auditor, county treasurer, county recorder, sheriff, county attorney, county surveyor, or coroner, the county board shall fill it by appointment. For that purpose it shall meet at the usual place of meeting, upon one day’s notice from the chair or clerk, which shall be served personally upon each member in the same manner as a district court summons. The person appointed shall give the bond and take the oath required by law, and serve the remainder of the term, and until a successor qualifies. When a vacancy occurs in an office that has a chief deputy or first assistant, the chief deputy or first assistant may perform all the duties and functions of the office until it is filled by appointment by the county board.