If a vacancy shall occur in the membership of the board, due to death, resignation or other cause, said vacancy shall be filled by appointment. If the vacant membership be of appointive character, appointment for the unexpired portion of such term shall be made by the board of park commissioners, and if it be of elective character, it shall be filled by appointment by the elective members of the board, provided that the person appointed to the vacancy of an elective member shall be an employee. The persons so appointed to elective membership shall serve until an employee who shall be elected to serve for the unexpired portion of such term shall be chosen. Such election shall be held concurrently with and in the same manner as the next regular annual election.