The remote switch wiring harness on the Onan7500/8000 is known to suffer from moisture build-up, causing some of the wires to short. Yours apparently shorts the pre-start warm-up (normally done by pushing the Off side of the button) circuit to ON, causing the clicking sound that signals the warming cycle. I'm guessing that it cools off in the evening and condensation forms in the wiring to trigger it.
I've heard that people have fixed it by thoroughly drying out the wiring with a hair dryer, but don't know how easy/hard that is or if its a reliable fix.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC