Vacancies in the office of Council members shall be filled within thirty (30) days by vote of a majority of the remaining members of Council, by the selection of a qualified elector who has resided in the municipality for at least one year immediately preceding such appointment. If Council fails to make this selection within thirty (30) days, the Mayor shall make the appointment. Such person so chosen shall serve until the next regular City Council election, occurring not less than 100 days after selection. At such election, a successor shall be elected to serve for the unexpired term, if any; if not, for a full term.