Example 1
No matter how hard the stand-up comedian tried, he couldn't elicit a response from the stone-faced audience.
Tough crowd. In this example, elicit is the way to go because the comedian is trying to draw out a laugh (or maybe even some spirited heckling?) from the audience.
Example 2
Darren believes illicit activities are taking place in his mysterious new neighbor's house, so he always has his binoculars at the ready.
Haven't we heard this story before? Maybe in the classic Hitchcock film Rear Window or the not-quite-a-classic Shia LaBeouf film Disturbia? Either way, illicit is the right word for this well-worn plot because it means the same thing as illegal.