Late last year, T. Boone Pickens was back at it, drilling for oil. On his 65,000-acre ranch in the Texas Panhandle, an expanse full of wildflowers and rolling hills, Mr. Pickens, 89, had erected a $6 million rig and started pumping fracking fluid into the earth. Decades past his heyday as a self-made oil mogul and old-school corporate raider, his fortune and his public profile diminished, Mr. Pickens was still hoping to strike it rich, just as he had done some 60 years ago as a young wildcatter in Amarillo. The well has begun producing, but Mr. Pickens — who...