A majority of the boards of police shall constitute a quorum; and the failure or refusal of the mayor or acting mayor of said cities to qualify or act hereunder shall in no wise impair the right or duty of said commissioners to organize and proceed as herein provided in sections 84.010 to 84.340. In case a vacancy shall occur on said board, the same shall be filled by the governor of the state of Missouri forthwith, after having been notified that such vacancy exists.