COTTONWOOD HEIGHTS, Utah — Mitt Romney never could resist a race.

Since dawn, half-marathoners had been whipping through a mountainside fog here, a short drive from the home he keeps, some 2,000 miles from the office he wants.

Mr. Romney stood just beyond the finish line, bopping in his jeans-and-flannel finest, smiling back at the runners like a distant relative at a wedding, waiting to be greeted. “Well done, well done, congratulations,” he said, handing medals to participants who may not have won in the end but plainly tried their hardest.

He clapped and shoulder-patted. He whiffed on a high-five. He studied the fingers of a woman unlocking her cellphone to take a picture with him, and guessed at the passcode. “Seven-six-four-three-nine-nine!” Mr. Romney shouted.

He laughed. People seemed confused. The camera clicked. Mitt Romney was back.

Six years after a presidential election defeat that loved ones expected to end his political career — and nearly a quarter century (and four campaigns) after his wife, Ann, swore she would “never” abide another run — Mr. Romney wants in again.