N.C. Gen. Stat. § 160A-70

At the organizational meeting, the council shall elect from among its members a mayor pro tempore to serve at the pleasure of the council. A councilman serving as mayor pro tempore shall be entitled to vote on all matters and shall be considered a councilman for all purposes, including the determination of whether a quorum is present. During the absence of the mayor, the council may confer upon the mayor pro tempore any of the powers and duties of the mayor. If the mayor should become physically or mentally incapable of performing the duties of his office, the council may by unanimous vote declare that he is incapacitated and confer any of his powers and duties on the mayor pro tempore. Upon the mayor's declaration that he is no longer incapacitated, and with the concurrence of a majority of the council, the mayor shall resume the exercise of his powers and duties. In the event both the mayor and the mayor pro tempore are absent from a meeting, the council may elect from its members a temporary chairman to preside in such absence.