GNP has a special place in my heart... I was lucky enough to be part of a team the NPS supported to reconnoiter the brand new Guadalupe Ridge Trail, a 100-ish mile trail that connects GNP and Carlsbad NP. Officially, the trail starts at the top of Guadalupe Peak, descends to Pine Springs, up Hunter Peak (but not to the summit), then down McKittrik canyon, north into Lincoln NF, east into Carlsbad NP, though the park, ending at Whites City. The NPS supported us with a couple of water caches. One of our jobs was to scope out springs, and we found a handy one. We submitted a lengthy report to the NPS, a couple years later, the trail was made official.
Here's an article... Our team is mentioned about 2/3rd of the way down, with an interview with Jennifer Roach (Gerry Roach's wife, Gerry is kinda famous her in Colorado, a world class mountaineer).
https://www.newmexico.org/nmmagazine...e-ridge-trail/
Enjoy your trip! Make sure you get there early and can snag a campsite at Pine Springs. I slept on a picnic table a couple nights after our GRT thru hike, woke up to a marvelous sunrise both mornings.