I have reviewed the Texas timezone history before 1970.

I attach my result, which proposes two additional Texas zones America/Houston and Amerca/Amarillo.

I think there is an error in the current tzdata/northamerica file regarding Texas. It claims that Texas follows America/Chicago.
But this is not the case as Texas had no DST in 1936, as Chicago did.

Please check my data and my typing, as I am a bad typist.