At KIBS in Bishop, I used The Beatles' "Good Night" as a buffer between the last hit and the religious minute "Be Still and Know", which then went straight into the National Anthem. I laid the 30-second pre-recorded signoff recorded years before, which used to run cold between "Be Still and Know" and the National Anthem, over the intro to the Beatles track.
And then, the deep baritone voice intones: "Be still....and know."
The only other station I worked at that wasn't 24/7 was KUKI, Ukiah, where we signed off at midnight. There was no pre-recorded signoff and no formal script. I was told that all that was legally necessary was a station ID, so I'd say goodnight over the intro to the last record, and then either at the cold ending or as it faded, say "It's 12 midnight at KUKI, Ukiah".
There was one other sign-off I was involved with. At KTNV-TV, the ABC station in Las Vegas, we signed off one night a week at 2:00 a.m. for maintenance (I believe it was early Monday morning). Our recently-arrived Creative Services person wanted to do a longer-form signoff, but less formal and stodgy than the old one, done over a station ID slide.
Her idea was a really artsy montage of the city lights at night and since she knew I'd been in radio, she asked if I had any ideas for music. I immediately suggested the Box Tops' "Neon Rainbow", which she wasn't familiar with. I played it for her, and that became the signoff, with the verbal signoff laid over the 20-second fade at the end.
Because it was 1985, we actually got calls and letters from people who said they kept tuning in at the end of "that music video show you guys have on" and wanting to know when it started.