The historic marker here explains this popular little shrine:
This is the only shrine in the United States dedicated to the soul of a sinner buried in unconsecrated ground. It is affectionately called “El Tiradito” – the castaway. The many legends about its origin all involve a tragic triangle love affair in the early 1870s. The mysterious powers of El Tiradito are still an important part of local Mexican lore and culture. This site is on the National Register of Historic Places.People still come to light candles and leave notes in the niches in the wall behind.
Location: The east side of Main Avenue between Cushing and Simpson (here's a Google Maps satellite view).
Hours: I'm not sure there are formal hours, but I'd suggest daylight or early evening.