If, during a recess of the Senate, there is a vacancy in an office filled by appointment by the Comptroller by and with the advice and consent of the Senate, the Comptroller shall make a temporary appointment until the next meeting of the Senate, when he or she shall make a nomination to fill such office. Any nomination not acted upon by the Senate within 60 session days after the receipt thereof shall be deemed to have received the advice and consent of the Senate. No person rejected by the Senate for an office shall, except at the Senate’s request, be nominated again for that office at the same session or be appointed to that office during a recess of that Senate.