During any period when the Mayor shall be absent or inaccessible or unable for any cause to perform his or her duties, the Vice Mayor shall be the Acting Mayor and shall also continue as a Councilman with all the powers and duties of a Councilman. In case the office of Mayor shall become vacant, the Vice Mayor shall thereupon become Mayor and his or her office as Councilman shall become vacant, and he or she shall serve as Mayor for the unexpired term or until the beginning of the term of a successor duly elected as hereinafter provided.