The governor shall appoint a director of health and in all cases of appointment of the director of health the governor shall while the senate is in session, notify the senate of his or her appointment and the senate shall, within sixty (60) legislative days after receipt of the notice, act upon the appointment. If the senate shall, within sixty (60) legislative days, vote to disapprove the appointment it shall notify the governor, who shall forthwith appoint and notify the senate of the appointment of a different person as director and so on in like manner until the senate shall fail to vote disapproval of the governor’s appointment. If the senate shall fail, for sixty (60) legislative days next after notice, to act upon any appointment of which it has been notified by the governor, the person appointed shall be the director. The governor may withdraw any appointment of which he or she has given notice to the senate, at any time within sixty (60) legislative days thereafter and before action has been taken thereon by the senate.