WASHINGTON—The FBI investigation into the sexual-assault allegation against Supreme Court nominee Brett Kavanaugh could hinge on a calendar entry he wrote decades ago, and a small group of people at a house party where Christine Blasey Ford says she was attacked.

The sudden turn of events Friday intensified the spotlight on Mark Judge, a Georgetown Preparatory School classmate of Judge Kavanaugh’s whom Dr. Ford says was in the room at the time of the alleged attack in the early 1980s outside Washington.

Dr. Ford said that when Judge Kavanaugh had her pinned down, a laughing Mr. Judge jumped on top of them, allowing her to escape. But Mr. Judge has said in a letter submitted to the Senate Judiciary Committee he has “no memory of this alleged incident.” His lawyer, Barbara Van Gelder, said Friday that he “will answer any and all questions posed to him by the FBI or any law enforcement agency.”

Mr. Judge, 54 years old, has chronicled his hard-partying ways and once wrote of a character, “Bart O’Kavanaugh,” who was so drunk he threw up in a car and “passed out on his way back from a party.”

Judge Kavanaugh on Thursday dismissed his friend’s writing as fictionalized and while describing him as funny, gifted and popular, noted Mr. Judge “developed a serious addiction problem that lasted decades.”