Waiting to let the penny drop is a good technique, and it can be used for comedic and dramatic purposes. It's a little easier to do with comedy, for if the laugh is good enough the audience will be more than willing to accept any delays revealing the twist. For an example, here's Monty Python's "The Pope and Michelangelo" sketch*:
Now, logically the Pope would be more upset by the three Christs than anything else. But it's funnier for the three Christs to be revealed after we've heard about the Jell-o, kangaroo, and twenty-eight disciples. It doesn't make sense, but no one cares because the comedic effect is so good.
It's a bit trickier with drama, but it can be done. A stellar example is Ray Bradbury's short story "The Aqueduct." I'm unable to find an online version of it, but do yourself a favor and go read it right now. I'll wait.
You're back? Good. Wasn't that a doozy? Though it's a very short story, it does so many things so well. First of all, that revelation. The first time I read the story, I actually screeched, something I rarely do. I hadn't seen it coming, and the implications of that revelation are so terrible that I was truly sucker punched. Furthermore, when you go back and re-read the story, it's clear that Bradbury did not cheat when writing that story. You might think he did, but go back and read it again. Pay close attention to the word choices. He does not cheat. Furthermore, he drops that penny and trusts his reader to know what that penny means.
How do you know when it's time to let the penny drop? Use your instincts on the first draft or two, then let your first readers tell you. If they laugh, or screech as the case may be, you've done it right.
* Yes, I am well aware that Leonardo Da Vinci painted "The Last Supper."