A few months ago I noticed a small water stain appearing where a
plaster crown molding meets the ceiling. Recently I noticed a
dripping noise after I shut off a sink in a bathroom that's more or
less above the stain. I might not have noticed it sooner because
there's usually a lot of noise from the bathroom vent fan.

Before I call a plumber or have the ceiling or wall ripped open, I'd
like to find out if the drip actually indicates a leak, and not just
normal water draining through the drain pipe. If I run the sink for
10 seconds, then shut it off, the dripping starts about 15 seconds
later, and continues for about another 15 seconds, at a rate of about
3 drips per second. I can hear it from the bathroom as well as from
the downstairs room. The plumbing is about 20 years old, in a house
that's much older.

Are there any tricks to find out what's going on?

Jimmy