When the General Assembly is not in session and when no other provision has been made for filling any vacancy in an office, appointment to which is made by the General Assembly or either branch thereof, whether or not on nomination by the Governor, or appointment to which is made by the Governor with the advice and consent of the General Assembly or either branch thereof, the Governor may fill the same until the sixth Wednesday of the next regular session of the General Assembly, and until a successor is elected or appointed and has qualified. The Governor may fill any vacancy in any office to which he has power of appointment, provided the Governor may not appoint a person who was nominated for an appointment subject to the advice and consent of the General Assembly or either branch thereof and whose nomination was rejected by the General Assembly or either branch thereof during the last preceding regular session of the General Assembly to the same or similar vacancy unless the General Assembly is in regular session.