I'll do this in two parts.
I have found Rocky Mountain Bighorn Sheep in the White Mountains of Arizona, but have had trouble finding Desert Bighorns. They always seemed more elusive. Desert Bighorn Sheep have adapted to the desert and are quite unlike their Rocky Mountain cousins.
The Desert Bighorn Sheep can go three weeks without water. That means they can stay high up in the mountains far from sight most of the time. I had looked many times in many places: Cabeza Prieta, Cibola, Imperial, and Kofa National Wildlife Refuges, Barry Goldwater Range, Yuma Proving Ground, and Organ Pipe Cactus National Park, all of which have fairly substantial populations (200 to 800).
What you have to do is put yourself in the place with the most potential; meaning: time of year, time of day, and rugged mountainous terrain. The Yuma Proving Ground just north of Imperial NWR was the answer. There is but one road into this area starting at Imperial NWR. After about five miles (through Imperial) you reach a desolate area of the YPG. This is a 4x4 high clearance "road" only. Definitely not for the faint of heart. I had done this three times before without luck. The first time I blew out a tire and had to return 115 miles to the nearest city (Yuma) to get it replaced. The next two times I made it all the way to where the road dead ends. This is gorgeous country. And I had it all to myself.
You drive up into the mountains. The mountains aren't tall, maybe 200-400 feet above ground level. But, they are very rugged which makes them perfect bighorn terrain. Each time I had gone through this one spot, I would say "if I were a bighorn sheep, I would want to be here."
NOTE: There is a wonderful book, "Counting Sheep: 20 Ways of Seeing Desert Bighorn" which is a collection of 20 essays from writers who also love nature and wildlife and who went out searching (some finding) the desert bighorns.
I have found them several times in this area, plus Canyon Lake along Apache Trail, east of Phoenix.