‘Get back across the border or you will be shot.’
Whoops... :)
Texas Penal code Title 7, Chapter 30 defines criminal trespass.
As long as these individuals are asked directly by the property owner to defend his private property against criminal trespass, they are theoretically operating under the law.
I say "theoretically" because in August 2001, Samuel Blackwood was convicted of homicide for killing an illegal immigrant who crossed the border and stopped at his ranch to ask for food and water. Blackwood shot at the illegal and hit him in the back of the thigh. The illegal bled to death. Blackwood tried to claim self defense. He was sentenced to a probated 180 days.
Again, they need to conduct themselves very carefully.