I'd be inclined to snake it first and see how that affects it. Might be some hair or other gook that's causing the liquid to drop into the stack.

Do you see any evidence of moisture? That would be my guideline. And this one is more difficult, but does the drip sound like it's outside the drain pipes...as if it's dripping directly on the backside of your wall surfaces, etc.?

My neighbor had such a leak which she ignored for 2 years until she started to see evidence of moisture in the bedroom ceiling below. When the wall was opened up there was considerable structural damage to a support beam, as well as mold growing in the ceiling. My advice is to bite the bullet now and open a small section of wall to see what you can see. If you have a vanity you could cut into the wall at the back of the vanity. When you have to close the wall back up, you could simply screw a 1/4" plywood panel in place to cover the hole and not have to bother with a time consuming repair to a visible part of the wall.

Are you sure it's not the PVC/ABS drainpipe rubbing against structure as it expands/contracts from water?

Hi, If you hear the drip after you shut off the water you might have cast iron drains they transfer sounds realy bad. When the plumbing finishes draining the noise will stop but it doesn't happen right away.
Woodbutcher

I've read in the past that sometimes a central heat and AC system installer will route the AC condensate drain line into the household drain system, instead of to an outside drip. This has the drawback of creating just such a nuisance drip noise as you describe. You might want to check this out first.