A person holding a state office by appointment of the governor, or of the governor by and with the consent of the senate, may be granted by the governor, on the application of such person, a leave of absence from such office, without pay, for a stated period less than the remainder of the unexpired term. The office shall be deemed vacant for the purpose only of filling it, in the manner provided by law, for a term expiring at the end of such period. At or after the end of such period, the person who is granted such leave of absence, if not then disqualified, may resume such office, its title, duties and salary for the unexpired regular term, without reappointment, and the interim incumbent, if any, shall cease to hold it. On or after the beginning of such period, such person, if otherwise eligible, may be appointed to and hold any other appointive office in the state service; but he shall resign therefrom before resuming such former office under the foregoing provisions. A person resuming such office shall file in the office of the department of state his statement in writing that he elects to and does resume it pursuant to this section.