Psychic impressions and uncanny feelings can be made very real in a game, in much the same way that magic and aliens and dragons can be. The cool thing is it's really easy. You just tell the player that they get a weird feeling about something, and tell them what it is.

It can be more or less reliable, depending on how well these things actually work in your setting. And you can drop them in at whatever moment is most dramatic. Or inconvenient. Or deceptive...

Transcript

GM: Obi-Wan, as you stalk the corridors of the Peace Moon, you feel a disturbance in the Force. A presence you've not felt in a long time.
Obi-Wan: I concentrate on the presence. Can I tell who it is?
GM: You sense a very powerful Force user. Familiar, but strangely confused. {on shot of Vader}
Obi-Wan: Hmmm. I really hope that's Yoda.
GM: You sense a long built-up wall of anger and rage. {on shot of Vader}
Obi-Wan: Oh. That doesn't feel like Yoda.
Obi-Wan: Could it be...?
Obi-Wan: No. No, that's impossible. He died on Naboo. I'm sure of it.
C-3PO: You're not right about everything, you know!
Obi-Wan: No. It must be someone else.
R2-D2: Oh for crying out loud! We all know who it is!
Han: Jar Jar? {over shot of Vader}