I was a Deputy for Eddy County, New Mexico back in the late 70’s. I remember a case that occured in Roswell where an individual was arrested for concealed carry. The individual had the weapon in an external holster attached to the belt. He was wearing a Denim jacket and the officer noted the holster just sneaking out from the bottom of the jacket. The outcome of the case was it was not concealed because it was in an external holster on the belt, if it was in an inside the waistband holster it would be considered concealed. We were directed not to hassel anyone carrying thus.
Things may have changed since then, but there is case law somewhere in the Roswell DA’s office.
P.S. Artesia is in north Eddy County.