A pair of local legislators will make yet another run at banning gun shows at the Cow Palace — and they say growing American revulsion at mass shootings, particularly at high schools, puts momentum in their favor.

The cavernous, state-owned exhibition hall in Daly City hosts five gun shows a year, the most recent in April, but those shows have drawn a growing number of protesters as gun massacres proliferated throughout the nation. State Sen. Scott Wiener, D-San Francisco, is now proposing legislation that would ban the sales of guns or ammunition at the hall, beginning in 2020.

“The environment has changed,” he said in an interview. “As more schools are being shot up, as more kids are being murdered, we need to protect our community, and that means fewer guns. I’m hopeful that we will be able to persuade the governor that this is a good idea.”

Wiener said he has “nearly universal local support” from communities surrounding the Cow Palace, and he hopes to ride the wave of “an amazing outpouring of student activism around the country against gun violence and in favor of gun safety measures.”

He and his principal co-author on the bill, Assemblyman Phil Ting, D-San Francisco, will announce their effort — the fourth attempt at a Cow Palace gun show ban since 2004 — Monday at the Bayshore Community Center in Daly City. Planning to be there in support will be 16-year-old Erica Cardoza.

Erica helped lead a demonstration at her campus, Daly City’s Jefferson High School, in March as high schools all over the nation reacted to the killings of 17 people at Marjory Stoneman Douglas High School in Parkland, Fla. Friday’s slaughter at a high school in Texas, in which 10 people were killed allegedly by a student, only reinforced her determination to stamp out gun shows at the giant hall, which happens to sit right in front of her home.

“This is a school community — Bayshore Elementary School is right next to the Cow Palace — and it’s crazy to be having a gun show right next to a school,” she said. “One minute the place is the setting for a rodeo, and the next it’s for selling assault weapons. It’s just not right.”

Erica said she supports the Second Amendment right to bear arms, but “as all these high school shootings have shown us, it should be more regulated and strict.

“It should be a privilege to own a gun — not just willy-nilly, like you can have whatever you want,” Erica said. “It needs to be responsible. We have regulations for cars — why can’t we have regulations on guns?”

Efforts to end Cow Palace gun shows have failed three times before in the state Legislature. The most recent rejection came in 2013 when Gov. Jerry Brown vetoed a bill by then-Sen. Mark Leno, D-San Francisco, that would have required local county authorities — who were opposed to the shows — to authorize them.

“The Cow Palace is important, and I’m not critical of the Cow Palace,” Wiener said. “They have to be financially sustainable ... but we have to balance that with our core values, and in the Bay Area people overwhelmingly do not support gun shows.”

Cow Palace officials directed queries to the man who has run the venue’s gun shows for 32 years, Robert Templeton, co-owner of Utah’s Crossroads of the West Gun Shows. He said each of the failed legislative efforts was misdirected, and the current one is no better.

Rather than focusing on reducing the proximity and number of weapons, he said, “we need to keep guns out of the hands of criminals, people who are too mentally ill to own them, and people who commit domestic violence.” Templeton also said the federal government should prosecute anyone who lies on a background check; more than 1 million people failed background checks over the past 20 years, according to the FBI.

“We have common ground on both sides,” Templeton said. “We all want to see this horrific gun violence stopped. We agree there. But in order to have a dialogue, we’ll have to be much less polarized than we are now.

“This recent senseless spate of school shootings has energized the people who would like to take away our gun rights, but we need instead to deal with the people who perpetrate violence and the potential perpetrators.”

Templeton said that there has never been a significant incident of violence at Cow Palace gun shows — which also offer fishing and other sporting gear — and that, contrary to some contentions, nobody can just buy a gun and walk away with it. Purchasers must undergo a 10-day waiting period and a background check, then pick up the weapon from an authorized dealer.

Ting rebuffed the reassurances, saying local objections to the gun shows should trump other considerations. Cow Palace gun shows, he said, are “the antithesis of what San Francisco and the Bay Area stand for.”

Sam Paredes, executive director of Gun Owners of California, said Ting and Wiener are just trying to score points with their voting base.

“Here we go again,” he said. “When you allow legislators to force on everyone else their own inclinations and predilections, and they decide what legal products can be used and sold at public venues, it smacks of social engineering and royalty. These shows are as safe as a knitting show or a coin show. But that’s not enough for these politicians.”

Chronicle staff writer

Melody Gutierrez contributed to this report.

Kevin Fagan is a San Francisco Chronicle staff writer. Email: kfagan@sfchronicle.com Twitter: @KevinChron