(1) If such vacancy occurs at least seventy-five days prior to the third Tuesday of the month preceding the end of the current official year, for the balance of such year.

(2) If such vacancy occurs less than seventy-five days prior to the third Tuesday of the month preceding the end of the current official year, for the balance of the year and, if the term of office does not expire at the end of such year, by further appointment to the end of the next official year. 4. Elective offices, which have been filled by appointment for part of the unexpired terms thereof shall further be filled for the remaining part of such terms by election at the general village election, if any, regularly scheduled to be held prior to the end of the period of such appointment. In the event no general village election is scheduled, a special village election shall be held on the third Tuesday of the month preceding the end of the period of such appointment. Such special elections shall be noticed, held and conducted in the same manner as a general village election. 5. A village trustee shall be eligible for appointment to fill a vacancy in the office of mayor. If a trustee shall accept such appointment, his office as trustee shall be vacant. 6. The village clerk shall, within three days after the appointment of a village officer, notify each person so appointed of his appointment and the date thereof, and that, in order to qualify: he is required to file his oath of office with such clerk together with proof by affidavit of his eligibility to hold such office before entering upon the duties thereof; and if an official undertaking be required by or in pursuance of law, that he is also required to file the same with such clerk and that upon his failure to do so, he will be deemed to have declined the office. In the case of a person appointed to fill a vacancy in the position of village justice or acting village justice, such notice shall further state that the filing of his oath with the county clerk of the county and with the chief administrator of the courts is also required. If an undertaking is required of a village officer after entering upon the duties of his office, the clerk of the village shall thereupon serve upon such officer, personally, a written notice that he is required to file such undertaking with the clerk within ten days after the service of the notice and that upon his failure to do so his office will become vacant.