Let's not forget that Jimmy Carter is also 94. Now if he were to die while Trump is president will he too order a shut down of government operations? I believe that given his growing estrangement from the GOP establishment his actions undertaken in an attempt to kiss up to the GOP old guards and elites.
Somethings are already set in stone.
Jimmy's funeral arrangements were made when he held presidential office.
He was president, regardless of public perception of his failures or successes, he was the president of the United States of America.
This thread is about George H.W. Bush.
You are right to wonder what current or future president would do upon Jimmy's death. Jimmy could live past 100.
(And to live without the burden of Alzheimer's to the ages of 95 Carter, 96 Dole and 94 Bush. Is a blessing.)