(a) The mayor in incorporated towns shall be ex officio president of the town council, shall preside at its meetings, and shall have a vote when the mayor's vote is needed to pass any ordinance, bylaw, resolution, order, or motion.
(b)
(1) The mayor in these towns shall have the power to veto, within five (5) days, Sundays excepted, after the action of the council thereon, any ordinance, resolution, or order adopted or made by the council, or any part thereof, which in his or her judgment is contrary to the public interest.
(2)
(A) In case of a veto, before the next regular meeting of the council the mayor shall file a written statement of his or her reasons for the veto in the office of the town recorder-treasurer to be laid before the meeting.
(B) An ordinance, resolution, or order, or part thereof, vetoed by the mayor shall not have any force or validity unless, after the written statement is laid before it, the council passes it over the veto by a vote of two-thirds (2/3) of all the council members elected thereto.
(c) If the mayor is unable to perform the duties of office or cannot be located, one (1) of the following may perform all functions of a mayor during the disability or absence of the mayor:
(1) The recorder;
(2) Another elected official of the city if designated by the mayor; or
(3) An unelected employee or resident of the city if designated by the mayor and approved by the city council.