Vince Gilmer was a well-loved doctor in rural North Carolina. One day, he borrowed his father from an assisted-living facility and committed patricide; he removed the fingers of the corpse, then he slept and went to his office. His nurses said that nothing about his behavior indicated distress. During questioning, however, Gilmer was a bad liar, and his plot was sloppy. It wasn't hard to build the case against the doctor. But had he made a deliberate choice to commit his murder on the border between North Carolina and Virginia (creating a "turf battle," redirecting beams of attention that would otherwise fall on his own apparent villainy)? Years later, Gilmer's rural-clinic successor (the writer of a new memoir, "The Other Dr. Gilmer") felt puzzled. Why would a smart man insist on being his own defense attorney? Why had Gilmer sabotaged himself in the courtroom? How could Gilmer commit murder and then show no signs of angst? Was he a sociopath? He talked a...