Stop when a match is detected. Economists don't hunt elephants, but they believe that if elephants are paid enough, they will hunt themselves. Statisticians hunt the first animal they see, N times, and call it an elephant. Operations Analysts measure the correlation of hat size and bullet color to the efficiency of elephant-hunting strategies, if someone else will only identify the elephants. Politicians don't hunt elephants, but they will share the elephants you catch with the people who voted for them.
Lawyers follow the herds around, arguing about who owns the droppings.
Vice-Presidents try to hunt elephants, but their staffs try to stop them. Presidents set broad elephant-hunting policy based on the assumption that elephants are just like field mice, but with deeper voices. Sales Managers sell elephants they haven't caught, for delivery two days before the season opens. Software Sales Reps ship the first thing they catch and write up an invoice for an elephant. Hardware Sales Reps catch rabbits, paint them gray, and sell them as desktop elephants.