(a) Except as provided by Section 31.123, each county clerk, city secretary, or secretary of the governing body of a political subdivision other than a county or city or the authority performing the duties of a secretary under this code shall keep that officer's office open for election duties for at least three hours each day, during regular office hours, on regular business days during the period:
(1) beginning not later than the 50th day before the date of each general election of the political subdivision or the third day after the date a special election is ordered by an authority of the political subdivision; and
(2) ending not earlier than the 40th day after election day.
(b) In this section, "regular business day" means a day on which the main business office of the county, city, or other political subdivision is regularly open for business.