No officer who has been dismissed from the military or naval service of the State shall be permitted again to enter the military or naval service of the State without the approval of the Governor of this State. No officer who has resigned for the good of the service, or who has been discharged under conditions other than honorable on account of inefficiency, or on account of absence without leave, shall be permitted to enter the military or naval service of the State without the approval of the Governor of this State.