I have no idea why you are posting Texas law or any other law for that matter to me, I am not a lawyer in Texas or anywhere else and I haven't even stayed at a Holiday Inn Express recently.
I do know the US Border Patrol regularly stops people walking and driving in my area and apprehends many for being in this country illegally. At times they fill buses with them. I also know the Border Patrol in this area does traffic stops and apprehends illegals, as well as having fixed checkpoints on the major highways along the border. They also hold impromptu checkpoints along the traveled roads in this area with other LE agencies.
I cannot tell you what authority they use to do this, nor do I care. If you are so concerned about LE authority to require ID or apprehend illegal border crossers I suggest you take it up with the appropriate agency. Or you could simply wander around near the border and when asked to produce ID, you can refuse to. I imagine if you do that you will find out whether they have the authority to do so or not. I just cooperate when stopped by any type of LE, and I don't even want to know what happens if I choose not to. If I ever feel the urge to not cooperate I am sure I will find out then.
US Border Patrol has special powers to arrest and detain within 50 miles of the Mexican border. 95% of our deportations are done from there
Well and good for you. Fortunately, there are some of us that care about our God given rights. You are welcome.
I cannot tell you what authority they use to do this, nor do I care.
This kind of active patriotism is encouraged by every socialist and Marxist regime. Be not afraid, for there are still a few Americans that will question unbridled authority. People that can not, or do not understand the authority that is granted by we the people to our civil servants; are an extreme danger to the republic. For you may wish to grant supreme authority out of wanton ignorance (not stupidity). As for me and mine, we choose free will. Even if you and yours deem it "illegal". For you see, I am an American citizen. Despite any protestations and provocations to the contrary, I have earned my citizenship; and have been extremely studious so as to never forfeit this treasure. And you?