The two titans of the Trump administration, President Trump himself and Vice President Pence, are squaring off in Arizona this week ahead of a primary election that could shed further light on the question of whether MAGA-world is moving on or clinging to its 76-year-old idol.

In a face-off similar to one in Georgia earlier this year, Mr. Pence has endorsed Karrin Taylor Robson in Tuesday’s primary for the Republican gubernatorial nomination, while his former boss has endorsed Kari Lake. Each of them are expected to appear at rallies for their respective choices in the state on Friday.

The Georgia tussle resulted in a rebuke for Mr. Trump. He supported David Perdue in the May primary and Mr. Pence campaigned on behalf of the incumbent governor, Brian Kemp. Reviled by Mr. Trump for refusing to cooperate in the president’s attempts to overturn the 2020 election results, Mr. Kemp won the race by 50 points.

Current polling in Arizona puts the race between the two GOP candidates in a virtual dead heat, with Ms. Lake enjoying a slight lead. Only three months ago, Ms. Robson was trailing badly — by 20 points in some polls — so her comeback has come as something of a shock to political observers in the state.

Election-watchers describe the struggle between the two candidates as one for the soul of the Republican Party in Arizona, which dominated the state’s politics for decades dating back to the days when Barry Goldwater was one of its senators. An influx of people from out-of-state and increasing urbanization in recent decades, however, has turned it slightly more purple. Mr. Trump won the state handily in 2016 but lost to President Biden in 2020 by 10,500 votes out of nearly 4.3 million cast.

A historian at Arizona State University, Brooks Simpson, notes that there are still more registered Republicans in the state than there are Democrats, but that the GOP is “divided between people that support Donald Trump and people that want the party to move on.”

Until 2020, the Arizona GOP had been moderating since the Goldwater days, as personified by its late senator: “With John McCain’s departure you really do have a fight for the heart of the Republican Party,” Mr. Simpson said.

Mr Trump’s choice in the primary, Ms. Lake, is a former television news anchor and an ardent supporter of the former president. She has parroted his lines about malfeasance in the 2020 election and has said she would not have certified that state’s vote had she been governor at the time. In his endorsement, Mr. Trump said Ms. Lake will “fight to restore election integrity.” He is scheduled to appear alongside her at a rally in Prescott Valley Friday.

The non-Trump GOP establishment’s choice, Ms. Robson, is a wealthy former lobbyist and developer who has poured $14 million of her own money into the campaign. Ms. Robson enjoys the support of the incumbent Republican governor, Doug Ducey, who is precluded by term limits from running for re-election.

“As Arizona Democrats pursue the reckless Biden-Harris agenda, Karrin Taylor Robson is the only candidate for Governor that will keep Arizona’s border secure and streets safe, empower parents and create great schools, and promote conservative values,” Mr. Pence said in a statement announcing the endorsement. He is scheduled to appear at rallies on her behalf at Phoenix and southern Arizona on the same day Mr. Trump is at Prescott Valley.

Although his grip on voters may have waned between 2016 and 2020, Mr. Trump maintains a firm hold on the party apparatus. After criticizing Mr. Trump’s efforts to overturn the 2020 vote, McCain’s widow, Cindy McCain, Mr. Ducey, and Senator Flake, a Republican who stepped down in 2017, were all censured by the Arizona Republican Party.

Another target of Mr. Trump, the state house speaker, Rusty Bowers, also was censured by the party this week, primarily because he had the audacity to testify before the House committee investigating the January 6 riots at the Capitol.

In a press release Tuesday, Arizona’s GOP accused Mr. Bowers of “direct violation of the Republican platform,” by killing all “meaningful election integrity bills” and supporting Democratic positions on  legislation dealing with education, immigration, and gender issues.