Each member of City Council shall be a citizen and qualified voter of the State of Texas and the City of Sweeny at the time of his or her election to office. No member of the City Council shall hold any other office or employment under the City government while serving on said City Council, or hold any paid employment under the City government within two years thereafter. Any member of the City Council ceasing to reside in the City shall be deemed to have vacated his or her position on the City Council.