The mayor shall be elected at the same election at which commissioners for Districts 1, 3, and 5 are elected under the provisions of Article 3 of this chapter and shall hold office for four years. The mayor shall be elected at large. The mayor shall qualify and take office in the manner hereinafter prescribed on the first Monday in October following his (her) election. The regular election for mayor shall be held on the second Tuesday of July, 1993, and every four years thereafter. The mayor elected at any such regular election shall on or before the first Monday in October following his (her) election make oath that he (she) is eligible for said office and will execute the duties of same according to the best of his (her) knowledge and ability. At any election for mayor the candidate receiving a majority of votes for the office shall be elected thereto. If at the first election a majority is not received by any candidate for the office of mayor, the two candidates receiving the highest number of votes shall be declared eligible for a second (run-off) election to be held on the second Tuesday next thereafter following the first election.