The truth of this matter is that every other provision of the original agreement between the Republic of Texas and the United States of America is recognized as valid. This includes offshore drilling rights that no other state enjoys. If the civil war rendered null and void that original agreement then all such provisions therein would be so invalid. They are not. The only legal position legitimately reasoned is that Texas still retains the right to split.

There is a provision within the constitution that allows any state to further subdivide with the approval of said state and the Congress. However in the case of Texas, Cogress has already given it's approval b way of the initial agreement. Thus, should Texas decide to split, it can do so at its discretion. Q.E.D.