Craig, here is a track map that shows the Cloudcroft branch diverging from the mainline just north of Alamogordo at Alamogordo Junction. The railroad bypassed La Luz and entered La Luz Canyon
for about a mile before turning into Fresnal Canyon. The Cloudcroft branch is labelled as A&SM (Alamogordo & Sacramento Mountain).
The curved Mexican Canyon Trestle should be easy to spot from the highway. It can be reached by trail from the visitor facilities where the highway enters Cloudcroft. The switchbacks visible on the far mountain side are now part of the trail system using the railroad grade.