Disorganized communications. Security threats identified but dropped. Vague instructions. Lack of follow-through.

These lapses are emerging as key reasons the U.S. Secret Service failed to protect former President Donald J. Trump from an assassination attempt at a campaign rally on July 13 in Butler, Pa., a New York Times investigation has found.

The agency’s failures at the Butler Farm Show grounds — where a gunman’s bullets grazed Mr. Trump’s ear, wounded two rally attendees and killed another — are expected to be laid bare in coming weeks in an internal assessment delivered by the Secret Service itself and in a report from an independent Senate investigation. The pressures on the agency have taken on even greater urgency in light of what the F.B.I. identified as another attempt on Mr. Trump’s life at his golf course in West Palm Beach, Fla., on Sunday.

Senator Richard Blumenthal, Democrat of Connecticut and the chairman of a Senate subcommittee investigating the security failures in Butler, said that what happened on July 13 was clearly preventable. “Some of the lapses,” he said, “are so egregious as to be almost unbelievable.”

Interviews with federal, state and local officials and a review of documents provide an outline of how the planning process left vulnerabilities that allowed a 20-year-old video game enthusiast to open fire on Mr. Trump.

Perhaps the most glaring problem was the multiple levels of deficient and confused communications between the Secret Service and the local law enforcement agencies it was working with that day. The most prominent of those breakdowns involve warehouses, owned by AGR International, next to the rally site. The gunman, Thomas Crooks of Bethel Park, Pa., climbed on the roof of one of them to shoot at Mr. Trump.