For this discussion I'm not interested in the yes or no politics of it. I'm interested in what it would actually be.
How tall, wide, what materials, etc. Optimal location i.e. right on the border or some distance in country.
How would it be staffed, maintained, and resupplied.
You know all those little details that we don't get to because of the overall shouting on the issue.
I call my idea the MAGA-No! LINE. (Make America Great Again-No (entry for you) Line)
For me if I was building it I don't see the need for one contiguous wall.
Why not a series of fortlets built from HESCOs and shipping containers spaced every so often that troops patrol out of.
Put the fortlets in the best location for crossing so they block those route directly and space them depending on how hard the terrain is to see into and drive over. Closer, harder terrain would have the fortlets closer together and with easier, open terrain you could space them farther apart.
Why HESCOs and containers? They're cheap, modular, and easy to work with. Plus you're not defending against an armed invasion. Just normal folks on foot mostly so you don't need the expense of a hardened site.
Resupply using trucks and cargo helicopters. Possibly build a railroad behind the MAGA-No! line to make resupply even easier.
Make sure the fortlets are comfortable (AC and cold houses) for the personnel and spend the extra to make sure they get good food. Also rotate the people out on no more than a weekly basis. And probably less than that. In addition make sure that all the staffers get a chance at being posted in the easier areas and take their turns in the harder areas. Keep slots open in the very best places (near cities or the coasts) open for top performers so they have something to compete for.
That's my basic outline. Like I said, no politics just practically about the structure itself.