Elephant Butte seems to be the named peak of the cowboy rim area. Just across the saddle to the west is Cowboy Rim Mountain which is a dozen feet higher in elevation. This peak is in a very remote area close to the Mexican border. Caution: Active smuggling is ongoing; crossed two fresh trails, both with multiple boot prints heading north. Direction of smuggling route points to the area around the now abandoned Winkler Ranch which sits east of Gillespie Mountain at the end of Cottonwood Road. Also be cognizant of where you park as the area does include lands belonging to the Diamond A Ranch. Park on NM State Trust Lands or BLM land. Saw no one, not even the border patrol in this area. I've made three visits to this section of the Animas mountains in the past 18 months and only saw a border agent once. As is often the case when hiking in Hidalgo county, it's rare to see anyone. Cell phone coverage is almost non-existent.

Hiking distance to Cowboy Rim is about 7/10 mile with a drop of almost 400 ft to the saddle. BTW, one of the smuggling routes is the saddle. There's a spring noted on maps east of the peak in Cowboy Creek. It was not running.