Joel Greenberg, a onetime county tax collector, disclosed to investigators that he and Mr. Gaetz had encounters with women who were given cash or gifts in exchange for sex, the people said. The Justice Department is investigating the involvement of the men with multiple women who were recruited online for sex and received cash payments and whether the men had sex with a 17-year-old in violation of sex trafficking statutes, people familiar with the inquiry have said. Mr. Greenberg, who is said to have met the women through websites that connect people who go on dates in exchange for gifts, fine dining, travel and allowances and introduced them to Mr. Gaetz, could provide investigators with firsthand accounts of their activities. Mr. Greenberg began speaking with investigators once he realized that the government had overwhelming evidence against him and that his only path to leniency lay in cooperation, the people said. He has met several times with investigators to try to establish his trustworthiness, though the range of criminal charges against him — including fraud — could undermine his credibility as a witness.