(1) All taxes due in the City of Gun Barrel City shall be payable at the office of the Henderson County Tax Collector, or at such location or locations as may be designated by the City Council, and may be paid at any time after the tax rolls for the year have been completed and approved. Taxes for each year shall be paid before February 1st of the next succeeding year, and all such taxes not paid prior to that date shall be deemed delinquent, and shall be subject to penalty and interest as the City Council shall provide by ordinance. The City Council may provide discounts for the payment of taxes prior to January 1st in amounts not to exceed those established by the laws of the State of Texas.
(2) Failure to levy and assess taxes through omission in preparing the appraisal rolls shall not relieve the person, firm or corporation so omitted from obligation to pay such current or past due taxes as shown to be payable by recheck of the rolls and receipts for the years in question, omitting penalty and interest.