Place it at the very end of a late-night edit, after the last joke or reaction, so it closes the scene. Follow it with a snore sound to show the character is already asleep, and keep any earlier reaction short so the goodbye stays the focus.
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This short Dutch clip says 'Bye deze jongen gaat slapen' in a plain spoken voice and lasts about three and a half seconds. It feels like a cheerful, sleepy sign-off, the kind of line that makes a late-night goodbye sound playful instead of abrupt. It comes from the Ad Looij meme.