(a) The mayor or, in case of his or her absence, the recorder-treasurer, shall preside at all meetings of the town council. The recorder-treasurer shall also be and act as clerk of the town. He or she shall attend all meetings of the council and make a fair, accurate, and correct record of all the proceedings, laws, rules, and ordinances made and passed by the council. The records shall be open at all times for the inspection of the electors of the town.
(b) In the absence of the mayor and recorder-treasurer from any meeting of the council, the council shall have power to appoint any two (2) of their number to perform the duties of mayor and recorder-treasurer for the time being.