SAN FRANCISCO — As soon as President Trump signed his executive order on immigration, some of the biggest tech companies went quiet. Their executives did not sign legal briefs, brandish statements or dissent on Twitter. They strove for business as usual.

This was the older, stodgier, less glamorous part of the tech universe. These executives are generally not household names. Most of the companies have little presence in the excitable consumer marketplace. Some are government contractors. Their workers tend to be more settled, less tempted by cool start-ups. Despite the companies’ sizable employment, the spotlight is not on them.

Among these firms are IBM, Hewlett Packard Enterprise, Qualcomm, Cisco, Dell and Oracle. When 127 companies signed an amicus brief last week in a Seattle court that said the executive order “violates the immigration laws and the Constitution,” none of these six firms were on the list.

Yet even at some of these companies, there are stirrings of defiance. In a few well-publicized cases, workers have noisily quit. Many more have chosen to remain but are agitating for an explicit corporate morality even as Mr. Trump considers a new executive order on immigration. They want their companies to make clear not only what they support but also, perhaps even more important, what lines they will not cross.

The activist push is being driven in significant measure by women, who are still fighting for their due in a male-dominated industry. But in an unlikely twist, the chief executives they are trying to influence at two major companies are female.

At IBM, a petition has been circulating that proclaims, “We have a moral and business imperative to uphold the pillars of a free society by declining any projects which undermine liberty.” The organizers say nearly 1,000 verified employees have signed.

This is a delicate subject for big tech companies, none more than Big Blue. Mr. Trump during the campaign explored the idea of a Muslim database, although his remarks were inconclusive. IBM’s punch-card technology, as detailed by the United States Holocaust Memorial Museum, was used by the Nazis in 1939 to do a census. That data, in turn, led directly to Adolf Eichmann’s Jewish Registry.

At Oracle, the Silicon Valley database giant whose first customer was the Central Intelligence Agency, three young women — none of whom has worked there for more than a handful of months — started a petition last week to encourage the company to join the amicus brief. Hundreds of Oracle employees have signed it.

“In some instances it is notable for a company to take a stand on an issue,” said one of the women, Irene Scher, a regional vice president of sales. “In this case, it’s notable not to have taken a stand.”

A co-chief executive of Oracle, Safra Catz, and the chief executive of IBM, Virginia Rometty, became advisers to Mr. Trump during the transition. “I know that you are committed to help America’s economy grow in ways that are good for all its people,” Ms. Rometty wrote to him in November. Ms. Catz said in December, “We are with him and will help in any way we can.”

The three friends who created the Oracle petition joined the company in August, when it acquired the company they worked for, Opower. They emphasize they are not at odds with their employer.

“This isn’t a criticism of Oracle,” said one of them, Rachel Kane, a sales executive at Oracle Utilities. “We’re giving them visibility into how individuals at the company feel.” Oracle declined to comment.

Both petitions echo the Never Again pledge, which nearly 3,000 tech workers publicly committed to during eight days in December. Signers agreed not to participate in the creation of any government database that would target individuals based on race, religion or national origin. Five of the nine people listed on as having worked to create the pledge, including the lead organizer, are women.

Cauvery Patel, a corporate strategy associate at IBM, said she believed “workplaces have a responsibility to society — to the clients we serve, the employees we hire and the citizens who are impacted by our decisions.” She said IBM had been “progressive” in encouraging women’s participation in technology and on other issues, but had not delivered on the immigration ban.

“IBM’s decision not to actively stand up to the Trump administration and condemn this policy is extremely disturbing,” she said.

At Hewlett Packard Enterprise, employees have been asking why it did not sign the amicus brief. Meg Whitman, the chief executive, responded Friday that “simply, we were not contacted to participate.” She indicated the company would be taking a more assertive role: “You can expect to see us add our voice.”

Dell and Cisco declined to comment. Qualcomm did not respond to a request for comment.

The internal debate at some of the big tech companies revolves around the question of engagement: Can you persuade more from the inside than the outside?

The pro-engagement position has been expressed by Elon Musk, the chief executive of Tesla and SpaceX and a member of the President’s Strategic and Policy Forum. In a handful of cases, people have said they are canceling new Teslas because they view him as working for the president.

“Activists should be pushing for more moderates to advise President, not fewer,” Mr. Musk responded on Twitter. “How could having only extremists advise him possibly be good?”

Mr. Musk said he had made sure that the travel ban was discussed “first and foremost” at a Feb. 3 White House meeting. A spokeswoman said no further details were available.

The answer did not satisfy everyone. As one critic replied to Mr. Musk on Twitter: “You are not advising Trump, you are giving him cover and validating his nonsense. You can do more good by taking a stand. Please.”

IBM released a statement that said Ms. Rometty had “conveyed the company’s views directly to the president and the secretary of Homeland Security” on Feb. 3, “including suggestions for how technology can help to promote both national security and lawful immigration.”

Ed Barbini, vice president for corporate communications at IBM, said no further details were available. He noted that the company said in December that it would never participate in the building of a Muslim registry. He declined to comment on the petition.

When a small group of IBM employees was drawing up the petition in November, it debated including a reference to the Nazis. IBM maintains that the accounts of its role in Hitler’s regime are overblown and incendiary.

The employees decided to refer to the episode obliquely but focus on a more positive example — the company president Thomas J. Watson Jr.’s Policy Letter No. 4, which resisted pro-segregation policies in the South in the 1950s.

“Watson sacrificed short-term business interests in order to be on the right side of history, something IBM takes pride in today,” the petition says.

Daniel Hanley, one of the organizers, said the goal was “to build an organization inside the company that can hold IBM accountable to our values, and serve as a model for tech workers at other companies.”

George A. Polisner, who worked in cloud services at Oracle, took his stand in December. He posted a resignation letter on LinkedIn, saying that unlike Ms. Catz, he was not there to “help” Mr. Trump.

“When his policies border on the unconstitutional, the criminal and the morally unjust,” he wrote, “I am here to oppose him in every possible and legal way.”

That was on a Monday. Mr. Polisner told his boss that he would work through Friday. After the letter became public, Mr. Polisner was fired immediately. At 56, he said, he probably would have worked at Oracle for a few more years if politics had not intervened.

“There are different ways to influence,” Mr. Polisner said. “It’s a personal decision. I chose this one.”

Ms. Scher at Oracle and her friends chose another.

“We all participated in the Women’s March,” she said. “I think it’s possible we’re feeling a heightened sense of civic responsibility.”