Before he climbed onto a rooftop and added his name to America’s bloody history of would-be presidential assassins, Thomas Crooks, 20, seemed to try to shrink from view.

Classmates who attended Bethel Park High School with him in the suburbs south of Pittsburgh described him in interviews on Monday as a smart but solitary and quiet student who walked through the halls with his head down, and who rarely raised his hand in class.

“He didn’t want attention, good or negative,” said Julianna Grooms, 19, who remembered first seeing Mr. Crooks when they were freshmen.

She and other former classmates have spent days texting one another, looking at old high-school photos and racking their memories for some clue about why Mr. Crooks opened fire at a Trump rally in Butler, Pa., on Saturday, killing one attendee, critically wounding two others and grazing former President Donald J. Trump in the ear. Mr. Crooks was shot and killed by the Secret Service.

On Monday, federal investigators did not provide any new answers about the gunman’s motives or ideology, but said they had been able to access to Mr. Crooks’s cellphone and were analyzing it, along with his other electronic devices.

The F.B.I. said it had finished searching the gunman’s home and car, and had interviewed nearly 100 rally attendees, law enforcement officers and other witnesses and received hundreds of photos and videos from the rally and other digital tips.