This following snippet is from The Art of Power by Jon Meacham, a biography on Thomas Jefferson,
It was nearing midnight as he wrote these words. He was suffering from his headache as the candle burned down and Jupiter, his personal slave, fell asleep. Perhaps it was the intimacy of the hour that encouraged his candor; perhaps he was boasting vainly. But Jefferson had some reason to say that “providence” had given men like himself the “means” to satisfy his sexual appetites—means he appears to have made use of.
I was wondering about the meaning of 'intimacy' in this context. From my search, the closest fitting meaning comes from Oxford Dictionary, defined as "A cosy and private or relaxed atmosphere". Could it be the right way to understand the phrase in this context?