I’m thinking there has to be someone who has studied these animals extensively at JTNP, and who might provide insights I’ve overlooked. I’ll dig a bit more and see if I can come up with anything.
Maybe this will be helpful:
Desert Bighorn Sheep - Joshua Tree National Park (U.S. National Park Service)
Three herds live in the park
The bighorn uses open areas of low growing vegetation near rugged terrain for feeding. This habitat preference divides Joshua Tree's bighorns into three more or less separate herds. The 120 animals that live in the Eagle Mountains at the far easterm boundary of the park is the largest herd. The second consists of about 100 animals and ranges through the main part of the Little San Bernardino Mountains. The smallest herd, which numbers only 30 animals, is found in the Wonderland of Rocks. Members of this last band are the ones most often seen by park visitors. Ewes seldom venture from their natal herd, but rams wander rather frequently.
Activity
The Desert bighorn is most active during daylight, moving to traditional bedding areas at night. During the summer bighorn rest during the hot midday, often on cliffs above their water source. Rest periods are also used for chewing cud.
Water is critical to bighorn survival. In early spring of years with good winter rains they get enough water from the grass they eat to go without drinking. At other times they must trek to a spring or water-holding depression at least every third day. Lactating ewes need to drink almost every day. Making the trek to water is the most dangerous part of a bighorn's life. It is in the narrow canyons, where most springs occur, that the adult sheep's only significant predator, the mountain lion,
Felis concolor, lies in wait. Most dead sheep found in the park are mountain lion kills.
ETA Scenario. Paul spots sheep at the oasis because it's the hot season where they need to come for water. Mountain lions follow sheep as this is the most vulnerable they are. Paul is chased by and needs to hide/escape lion and becomes wedged in crevice or lost. I doubt he was killed by a lion himself, because it's difficult to imagine there would not be evidence of this...something of his left behind, for example.