The evidence is even in the name. “Senate” is a term originating in Rome, and it roughly means something akin to a council of elders, with the implication of offering wisdom and guidance. It’s where concepts like advice and consent originated, which were later adopted by the U.S. Constitution.
(A lot of the lingo from the Roman Republic is found in the U.S. government. The seat of the Roman Republic was the Capitoline Hill in Rome – the origin of U.S. Capitol Hill.)