Now its my turn to do some guessing: if you were working in secret at Victorio Peak, you would be set up quite well to do so. There is a water supply on the surface nearby, and there are game animals to hunt. There might also have been a source for water under VP itself. If you found a rich subterranean placer under VP you would work in the cool shade, not in the desert heat, and you would do your work out of sight. If you stored away enough food, you might not have to go outside for weeks at a time! You might raise a family while this was going on, and several generations might have been involved.
BUT, when the Indians finally found you, they would not be happy with the fact you set up operations right next to their main base camp at Geronimo Mountain. So you and your family might be killed/tortured, and perhaps tied up and left to die of thirst and starvation just a few feet away from all the gold you and your family had worked to hoard over the years...
I don't believe you would be living underground for any extended periods - and for anyone who has not spent any time in a mine or deep cave, more than a couple days is an uncomfortable extended period in my opinion. It's inconceivable to me that you would choose to semi-permanently live underground, as it is not a healthy experience, physically or psychologically, in large doses. Legend has it that Indian slaves were kept en masse underground in some of the old Spanish mines and worked until they died, but this doesn't sound too smart as your help would be dying off rapidly. If you had unlimited replacements, it might work for a while, but the Indians near the mine would not be stupid, and it's hard to imagine they'd remain vulnerable to getting constantly abducted.
For the type of extended operation you're proposing, you would need a surface camp, in my opinion, and go underground to work for a day or so at a time at the most. You would need shelter - easy enough to erect. You would need firewood - easy at first, harder as time goes by. Many sites - not all - offer the advantages of water and game, but the game wouldn't last long, or at least you would be chasing it increasingly farther from camp as time went by. Also, people need more than meat to eat, at least after a few weeks. That means you need to either have some sort of a relationship with local natives to obtain grains, nuts, etc. (assuming there are native villages nearby), or you need to grow and gather your own food - not an easy task in the Southwest.
A 20-year secret operation is a real beast, but I've actually heard of one in the Southwest that lasted about five years. This alleged European group numbered about thirty professionals when they arrived. They allegedly took over a permanent native village about twenty miles from the mine - a site which was located, yes, in underground caverns. The outsiders kept much of their force in camp in order to compel the natives to maintain a food supply for them. The underground work was done by slaves stolen from the tribe. The troublemakers were chained to the wall at the entrance as examples to the rest, who were treated reasonably well if they continued to cooperate. From the beginning, tribal members who escaped the village, along with allies from other villages, waged sniper warfare against the group, gradually reducing their ranks. Eventually, the Europeans' were reduced in number to a point where they could no longer control the operation and they organized a retreat. Or so the story goes. It seems possible, but the mystery of it would be the identity of the Europeans.