There is no 'evidence' of the age of the girl, other than the claim of someone in prison who was giving out information to try to cut a deal.
So he had sex with a girl at the party in question, yes?
And we have a girl who says she was at the party who had sex with him. And another who says she saw them having sex. Both under oath. That's evidence, with quotations or without. Regarding the woman's actual age at the time in question, what kind of evidence do you need? Her birth certificate?
Gaetz might not be charged with paying a prostitute. Who cares? Even if it can't be proven beyond a reasonable doubt, it is still relevant as to his confirmation as the Attorney General of the United States. And you have to bury your head in the sand to conclude he wasn't paying for sex.
Now, if we want to discuss whether that should disqualify him, I'm open to it. But first, we need to agree on the facts. Gaetz has ducked and dived, and come up with some other interesting stories, but none of them detract from the fact that he had sex with a teenage girl--probably not knowing her exact age--at a coke party with a bunch of prostitutes. Nor do those stories contradict or call into question that he has a history of payments to women that look exactly like payments to prostitutes while having a friend involved in sex trafficking prostitutes.