The appointee shall serve during the entire unexpired term in the office in which the vacancy occurs if such office would in regular course be filled at the next General Election if no vacancy had occurred. If such office would not in regular course be filled at such next general election the vacancy shall be filled as follows: At the next General Election, if the vacancy occurs four months or more prior thereto, and at the second General Election after the vacancy occurs if the vacancy occurs less than four months before the next General Election after it occurs. The person so elected shall take office on the 1st day of January following his election.