GREEN BAY, Wis. — Donald Trump drafted NFL star Brett Favre to campaign with him in this electoral battleground and help solidify the former president’s appeal with men.

Mr. Favre took the rally stage with Mr. Trump just days after the GOP nominee campaigned in New York with tech billionaire Elon Musk and wrestler Hulk Hogan. Earlier Wednesday, famed astronaut Buzz Aldrin delivered a forceful endorsement of Mr. Trump.

“We have already had President Trump once. We have already seen Kamala in action. We can compare, and we know which is better,” Mr. Favre said.  “It would be insane to give Kamala four more years in office.”

“So it is time to bench Kamala and put in the star quarterback Donald Trump,” he said.

Vice President Kamala Harris has countered by appearing alongside former First Lady Michelle Obama and signing star Beyoncé, leaning into her appeal to women as she tries to make history as the first woman to win the White House.

The “gender gap” has been a fixture of U.S. presidential elections since 1980, with men favoring Republicans and women favoring Democrats. And the divide is going strong in the Harris-Trump showdown.

Analysts say Ms. Harris could benefit.

“Not only are women favoring her a bit more than men are leaning toward Trump, but women also make up a larger share of voters,” said Barry C. Burden, a political science professor at the University of Wisconsin-Madison. “That would replicate the results in 2020 when Biden won the popular vote nationally and in most battleground states.”

Ms. Harris thinks Mr. Trump’s sometimes rough rhetoric and the abortion rights issue will chase more women into her corner.

Mr. Trump is counting on that tough-talking persona, warnings about transgender activism run amok and his willingness to upend the Washington establishment to draw in men.

Polling is divided.

The latest New York Times/Sienna College national poll, which showed the race tied at 48%, found Ms Harris with a 12-point lead among women and Mr. Trump with a 14-point lead among men.

CBS News-YouGov also showed that Ms. Harris had a 12-point lead among women, and Mr. Trump had a smaller 9-point lead among men.

Charlies Franklin, director of the Marquette Law School poll, said his latest polling showed that non-college men are heavily pro-Trump, non-college women and college-educated men are evenly split, and college-educated women are very pro-Harris.

He said it comes down to how they break.

“Do non-college women end up voting more for Mr. Trump, like their male counterparts, do the college men end up voting more for Harris, like their female counterparts, or do they continue to split their vote?”

Former Wisconsin Republican Rep. Reid Ribble said Mr. Trump and Ms. Harris had been far more focused on playing the testosterone and estrogen cards than on curbing their losses with the opposite sex.

“I don’t think Harris’ messaging has been particularly driven toward men or necessarily directed toward men at all,” Mr. Ribble said. “I think she feels that her path to victory is to get as big a gender gap as she can. Likewise, I don’t think Trump is pandering or trying to get to female voters at all.”

“You’re dealing with, at this point, about 1% of the voting population that you’re trying to persuade,” he said. “So Trump’s trying to persuade that 1% male independent, and Vice President Harris is trying to persuade that 1% female independent because that’s all that is left to get.”

Both candidates need to strike a delicate balance between driving their key voters to the polls without scaring off others.

Mr. Trump’s daughter-in-law, Lara Trump, is leading a Team Trump Women’s tour and is warning women about the threat migrant crime poses and the radical left’s push to allow men to play women’s sports.

The Trump campaign this week promoted a letter to Ms. Harris from Patty Morin, the mother of Rachel, who was raped and slain on a popular trail in Maryland. An illegal immigrant has been charged in that case.

“Families in America deserve safety and peace, not this kind of devastation; Rachel’s story must not be re-lived,” Ms. Morin said in her letter.

Trump campaign spokesperson Karoline Leavitt said the Harris policy agenda has hurt women.

“Kamala Harris may be the first woman Vice President, but she has implemented dangerously liberal policies that have left women worse off financially and far less safe than we were four years ago under President Trump,” Ms. Leavitt said.

Ms. Harris, meanwhile, is running advertisements — including on male-dominated video game and sports betting websites — and has deployed businessman Mark Cuban, NBA Hall of Fame legend Earvin “Magic” Johnson, and rapper Eminem.

She’s also ditched her early campaign slogan of “joy” in favor of bitterly hostile TV ads against Mr. Trump.

That includes one in Wisconsin featuring narration from Doc Rivers, head coach of the Milwaukee Bucks and co-chair of “Athletes for Harris.”

“In this town, we’ve seen our share of hard times, heard our share of big promises,” Mr. Rivers says in the ad. “But empty promises don’t build cities. We do — with grit, sweat and cold beer.”

The ad dings Mr. Trump for failing to deliver his promise of a Foxconn deal to create thousands of jobs outside Milwaukee and for disparaging the state’s biggest city as a “horrible city.”

“When he talks [expletive], we know talk is all he’s got,” Mr. Rivers said.

Mrs. Harris has delivered a similar message over the airwaves in Pennsylvania, another blue wall battleground. It includes a Pittsburgh area spot featuring a lifelong Steelers football fan who says, “Donald Trump does not care about the working man whatsoever.”

“He is a little rich kid. He ain’t me. Little silver spoon boy Donald Trump: How is he relatable to me whatsoever? The guy literally lives in a county club. Do I look like a country club kind of guy?”