In the trial itself, the task of the jury was not to establish either sanity or insanity. Instead, following the procedure of the adversary system, the jury's task was to decide whether the prosecution had proved beyond a reasonable doubt that Hinckley was not insane. So, the jury was judging the prosecution's case, not Hinckley. Most people believe that the question of insanity ought to be relatively easy to establish. No, it isn't.
Insanity is foreign to psychiatry.
Psychiatry, like all of medicine, is an empirical technology. The premise of empiricism is that the universe exists as it is, and the task of scientists and other empiricists is to discover facts about it. By contrast, the law is a product of idealism. The premise of idealism is that there are ways the universe ought to be, and the task of the idealists is to invent ways of achieving that. Insanity is an invention of idealists.