In case the office of the mayor shall become vacant, a successor for the unexpired term shall be elected as mayor at the next regular municipal election, provided that (a) such election shall occur more than two years prior to the expiration of the unexpired term, and (b) the vacancy shall have occurred more than one hundred twenty days prior to such election. A president of Council who has become mayor pursuant to Section 4.1 may be a candidate to succeed himself or herself.