He didn't ask for it, but Gerald Ford didn't shirk the White House.
In fact, in 1972 President Nixon was searching for a replacement for Vice President Spiro Agnew who resigned under a bribery and tax evasion scandal. Using the 25th Amendment Nixon called Congressman Ford who, at the time, was mulling retirement after a quarter of a century on Capitol Hill.
Nominated in October of 1973 and installed in December of that year Ford would go on the road sticking up for Nixon and raising money for the Republican party. Suddenly, in August of 1974 he became the President when Nixon resigned in disgrace.
Ford appointed Nelson Rockefeller as his vice president, famously pardoned Nixon and held off Ronald Reagan to earn the GOP nomination. He picked Kansas Sen. Bob Dole as his 1976 running mate, engaged in the first presidential debates in 16 years and promptly lost the general election to Jimmy Carter, making the owner of that flag pin very happy.
In retirement he was involved with many charities and served on a handful of boards. He considered running again for the White House and, separately, serving as the V.P. on Reagan's 1980 ticket, but neither thought became a reality.
This section is intended for presidential candidates, but First Ladies earn a following and, after reading this Smithsonian Magazine article on Mrs. Ford I'd concern her a nominee.
Ford died in 2006. His old running mate, Sen. Bob Dole would stay in the Senate and later lose the 1996 race to President Bill Clinton.