From a distance, as it hugs the hilly terrain, the fence looks almost decorative — a rambling, rust-colored abstraction. A thin ribbon of road runs alongside, its sandy surface kept impressively smooth by the U.S. Border Patrol, who drag it with old car tires twice a day, the better to spot telltale footprints. The road winds in and out of sight, deserted except for an occasional figure on horseback, usually a sunburned tourist from the adjacent dude ranch, relishing the Western-style emptiness.

Closer up, the fence is less abstract, more forbidding. The steel posts are eighteen feet high, separated by a…