Thomas Gilbert Jr. repeatedly interrupted testimony from his mother, who said he had been mentally ill for years before his father’s murder. In the summer of 2009, Thomas Gilbert Jr. cut a handsome figure in his Princeton graduation gown as he posed for a photograph with his mother, sister and father — a hedge fund founder well-known in wealthy Manhattan circles. This week, Mr. Gilbert, 34, was hunched over the defense table in a Manhattan courtroom, a shadow of the strapping blond surfer he once was, with unkempt beard and hair, rocking in his chair and staring downward.