In "Dear Tomorrow" by Simon Clark, the presenters of a regular live TV show plan to broadcast from the top of a mountain, asking any time travelers who find the archived show to travel back to this date and join them on the mountain. Heavy rain prevents the broadcast. The main event in the story is that a widower and a widow who had participated in the show because of their respective bereavements start to get together and move on, leaving the past behind, into tomorrow. The story hints that one person present is in fact a time traveler but I think that this was unnecessary.
If any time travelers see the archived show, then they will also see whether they appear on the show. If they do not (see themselves) appear, then they will not (travel back to) appear.