Equestrian campground
If there's no availability at the other campgrounds at Guadalupe Mountains NP, the rangers may take a pity on you and put you up at Frijole Horse Campground (out at the stables) if there are no reservations. Definitely try to reserve a site at the other campgrounds first.
If you're lucky to get a spot, there are two campsites; one is on a raised platform. There are parking spots, one is a handicap spot.
The toilets are standard. You hear coyotes celebrating at night. The sunsets out at the stables make you feel like a cowboy/cowgirl/cowperson.