To play the role of detective, to gather facts and information usually in the traditional Sherlock Holmes inconspicuous way.
To investigate in the manner of a detective.
A proper Sleuth needs to be intelligent, witty, and always a few steps ahead others. In fact, he never reveals all his discoveries or conclusions. His wisdom is his greatest asset and he needs to hide that wisdom if he expects to be hired for his services.
An outsider that is too awkward to introduce themselves, but is obviously intrigued and won't stopstudying your every move from a safe distance. They are usually unaware that you are aware.
Every so often I look over the balcony and see the same goofy sleuth peeping up at the party.
A detective like person, capable of finding out (or stealing) useful information, often in under-handed ways. "Sleuthing" is the act of being a sleuth.