You gotta figure that the Guadalupe Peak is a LONG way from Odessa and it isnt going to be made by foot or horse in several days, more like a month.
There is a far more logical explanation to his finding gold and that is the north south trails the Spanish used to get from Albuquerque to Mexico City, and the strong possibility (if this story is true in any fashion) he actually found a lost, abandoned mule pack with ore in it. A few days travel by foot or horse, less than a hundred miles, and that would barely get him to the Carlsbad area and those are the closest mountains.
I figure, if the story is true, he stumbled on a 1600's or later Spanish pack mule, or several, that were lost or was wiped out by Indians. Think about it, 'gone for a few days and he came back with raw gold ore', not ore - rock specimens. The closest possibility for 'placer gold' is the Pecos river (70-80 miles west) and there is NO gold in it in Texas or southern New Mexico. He wasnt going to 'mine' that in a few days. The Spanish did that though. Crushed and screened out the gold as well as they could then packed and shipped it.
Take a look at the New Mexico history articles on where gold has been found and mined, not a lot in the Guadalupe Mts. I think I recall a small shaft nw of Carlsbad about 10 miles in the foothills, but I know many people have diligently searched those areas for gold and found nothing.
It is a bit more plausible that the guy stumbled on the 'Horsehead Crossing' French gold and there was some raw ore in it. I havent read anything anywhere that would support that though as all that was supposed to be silverware and gold objects. That would be about 3 - 4 days travel SW from Odessa on foot.