It’s not double jeopardy. Hinkley was found not-guilty due to insanity for the attempted murder of Ronald Reagan, James Brady, et al. Now that James Brady has died, there is a new fact that he has died from the effects of the injuries he sustained in 1981. It’s a new crime.
The jury ruled him insane 33 years ago. How can you rule him sane 33 years later? No new crime, just a continuation of the same crime.