The Other "Mad Jacks"

In his book, Curing Hiccups with Small Fires: A Delightful Miscellany of Great British Eccentrics, Karl Shaw writes about two other legendary characters who have been nicknamed "Mad Jack". In chapter two "Sporting Eccentrics" we read about John "Mad Jack" Mytton (1796-1834) and in chapter three, "Religious Eccentrics" we learn about the Rev "Mad Jack" Alington (1795-1863). 

What does John "Mad Jack" Fuller (1757-1834) have in common with these two gentlemen?

1. They all lived in England at the same time. Fuller and Mytton died within 11 days of each other. 
2. All three inherited vast fortunes and country seats as young men.
3. Fuller and Mytton were both Members of Parliament.
4. Unconventional thinking and eccentric behavior has made each of them a local legend. 

John Fuller is not mentioned in Shaw's book. He may have been a larger than life, boisterous character who did things his own way, but he was not truly "Mad" in the real sense of the word. As for Mytton and Alington, I'll let you be the judge.