When a vacancy occurs in a public office, the office and duties shall be assumed until the election or appointment and qualification of a successor as follows:
(1) Of the office of the county clerk, auditor and recorder or treasurer, by the senior deputy as designated in section 31-2006, Idaho Code. If no deputy is available, then the board of county commissioners shall assume the office until the election or appointment of a successor.
(2) Of any state executive officer, by the chief deputy, under the supervision of the governor.