He may not make it to the Oval Office. But he will make it into the history books, at least as an asterisk.

As Mike Pence formally kicks off his underdog campaign for the White House on Wednesday, he will become something almost unheard-of since the founding of the republic — a former vice president running against the president who originally put him on the ticket.

While it is not unusual for tension and even enmity to develop between presidents and vice presidents, never before has a No. 2 mounted a direct challenge to a onetime running mate in the way that Mr. Pence is taking on former President Donald J. Trump for the Republican nomination next year.

Vice presidents, after all, typically owe their national stature to the presidents who chose them, and even if they are not especially grateful, they rarely find it politically feasible to compete with their patrons. But Mr. Pence is gambling that Republican primary voters may eventually grow weary of Mr. Trump and turn to the other member of their party’s 2016 and 2020 tickets.

“Having a former vice president contest the president he served for their party’s nomination in contested primaries is like a 234-year flood,” said Joel K. Goldstein, a specialist on the vice presidency at the St. Louis University School of Law. “It doesn’t happen.”

“Defeated presidents don’t run again in modern times,” he added, “and vice presidents tend to inherit support from their administration’s supporters, not become pariahs to them” as Mr. Pence has since defying Mr. Trump’s efforts to overturn the 2020 election.

The broken relationship between Mr. Trump and Mr. Pence is itself a historical anomaly, of course. Mr. Trump sought to pressure Mr. Pence to claim the power to effectively reject Joseph R. Biden Jr.’s victory in the Electoral College, a power the vice president said he did not have. Mr. Trump was so angry that he publicly excoriated his own vice president, prompting a mob to hunt for him while chanting “hang Mike Pence” on Jan. 6, 2021. According to testimony, Mr. Trump suggested to aides that maybe his supporters were right.

“The reason why no other vice president appears to have run against his president is that he was selected by the president, and there is almost always a personal bond stemming from a sense of loyalty and gratitude,” said Richard Moe, who was the chief of staff to Vice President Walter F. Mondale. “I can’t think of another vice president who was treated more disrespectfully than Pence was by Trump.”

There are no precise parallels to the current situation. In 1800, Vice President Thomas Jefferson challenged President John Adams, defeating the incumbent’s bid for a second term. In those early days of the republic, however, the vice president was not the president’s running mate, but the second-highest vote recipient in the previous election. Adams and Jefferson had run against each other in 1796, with Adams prevailing and Jefferson becoming vice president because he was the runner-up.

The 12th Amendment ratified in 1804 changed that system so that the vice president was chosen in tandem with the president as part of the same ticket. That did not mean they were always on the same team. Many tickets have been forged between rivals who had just run against each other for the nomination, including John F. Kennedy and Lyndon B. Johnson in 1960, Ronald Reagan and George H.W. Bush in 1980 and Barack Obama and Mr. Biden in 2008.

Some vice presidents grew hostile to the presidents they served under, as when John C. Calhoun openly opposed Andrew Jackson during the nullification crisis pitting South Carolina against Washington over a tariff. After being dumped from the re-election ticket in 1832, Calhoun resigned the vice presidency to take a seat in the Senate to resist his former ticket mate’s agenda. Still, Calhoun never challenged Jackson as a candidate.

In 1916, former President Theodore Roosevelt and his onetime vice president Charles W. Fairbanks both drew support on the opening ballots at the Republican convention but were not actively campaigning against each other. Hubert Humphrey and his 1968 running mate Edmund Muskie both ran in 1972 for the Democratic nomination, neither successfully. In 2000, former Vice President Dan Quayle ran against George W. Bush, the son of the man who put Mr. Quayle on the 1988 and 1992 tickets.

But the closest the country has previously come to a direct contest between running mates was in 1940 when Vice President John Nance Garner, a conservative Texan known as Cactus Jack and no fan of President Franklin D. Roosevelt’s New Deal, waged a campaign for the White House.

Garner was known for his love of whiskey, once noting that “I don’t get drunk but once a day.” He is most famous today for his sour assessment of the vice presidency, which he declared not “worth a bucket of warm spit,” or some variation of that.

Since no president to that point had run for a third consecutive term owing to the precedent set by George Washington, it was not entirely clear that Roosevelt would be a candidate in 1940, and he made no move to stop Garner or other associates from running. Still, there was no love lost between the two. “I see that the vice president has thrown his bottle — I mean his hat — into the ring,” Roosevelt quipped to his cabinet.

Garner, a traditionalist, had fallen out with F.D.R. over the president’s effort to pack the Supreme Court and opposed breaking Washington’s precedent. “As retribution, he declared that he would run for the 1940 presidential nomination, but he never put his heart into it, and no one took his candidacy seriously,” said Mr. Moe, who wrote “Roosevelt’s Second Act,” a book about the 1940 race.

Roosevelt played coy all the way up to the Democratic convention, when he finally arranged to be “drafted” to run again. Roosevelt swept to the nomination with 946 delegates. Garner finished third with 61.

That election ushered in another change. Until that point, the parties generally chose the vice-presidential candidates, but from then on the nominees effectively took over that decision. Roosevelt picked Henry A. Wallace, leaving Garner to retire to his Texas ranch.

At this point, Mr. Trump may regret the choice he made in 2016. But it is not clear that Mr. Pence will do any better than Cactus Jack did.