Deathwatch

Robb White's Deathwatch came out in 1972, and the Mystery Writers of America gave it an Edgar the following year, in their juvenile mystery category; the New York Times also put it on its list of outstanding books for the year.

Madec is a lawyer and a keen hunter who has won a rare seven-day permit to hunt bighorn sheep in the Mojave Desert. He takes on a shy college student called Ben as his guide. Ben knows the desert, since he is studying geology, and he needs the money, so he takes the job.

Then Madec shoots an old prospector by accident, and the two of them disagree about what to do next: Ben insists that the death has to be reported, and Madec has no intention of reporting it. Madec takes Ben's clothes from him, leaves him in the desert with nothing but his shorts, and goes back with a story ready that Ben had lost his mind; most of the book is the long contest between the two of them that follows.