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From back in the '70s, meaning to "forget it" or "never mind"

"You wanna go out with me?"
"Well, I'm kinda busy..."
"Okay, shine it on."
by Louisa D November 11, 2006
to act like it doesn't bother you
Ricky's behavior was uncalled for, but I knew it was best that I just shine it on.
by Joey Low January 25, 2008
abandon something or someone
Dates from the early 1970's, derived from waving goodbye, a similar hand motion to polishing something.
This project is no longer relevant. Time to shine it on.
by KitCur October 15, 2008