Constitution of the State of Texas 1876 Art. 3, § 9. President pro tempore of Senate;  election of Senator to perform duties of Lieutenant Governor when office vacant:  Speaker of House of Representatives

Sec. 9. (a) The Senate shall, at the beginning and close of each session, and at such other times as may be necessary, elect one of its members President pro tempore, who shall perform the duties of the Lieutenant Governor in any case of absence or temporary disability of that officer.  If the office of Lieutenant Governor becomes vacant, the President pro tempore of the Senate shall convene the Committee of the Whole Senate within 30 days after the vacancy occurs.  The Committee of the Whole shall elect one of its members to perform the duties of the Lieutenant Governor in addition to the member's duties as Senator until the next general election.  If the Senator so elected ceases to be a Senator before the election of a new Lieutenant Governor, another Senator shall be elected in the same manner to perform the duties of the Lieutenant Governor until the next general election.  Until the Committee of the Whole elects one of its members for this purpose, the President pro tempore shall perform the duties of the Lieutenant Governor as provided by this subsection.

(b) The House of Representatives shall, when it first assembles, organize temporarily, and thereupon proceed to the election of a Speaker from its own members.

(c) Each House shall choose its other officers.