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.