How do you have border control without fences?
You don’t.
Although fences are nice, the first rule of border security is to have armed men posted. Fences, walls, moats, minefields, and high tech surveillance are all useless without men on the ground. Wouldn’t take much more than two or three brigades of the regular Army, but that would be too sensible for DC!
Actually, most borders on the globe are marked by rivers and mountain crests -- and are without fences.
So far as the Rio Grande border is concerned, we can go to school on the nation that absolutely has to have a secure border: Israel.
Their border with Jordan is the Jordan River. And there is no fence. Instead, there are advanced observation posts, technological listening posts and a highly mobile border force.
This approach allows the farmers on both sides of the river access to its waters, while maintaining security.