Mystery water in wall

I thought I had a leak in my wall but here are the facts.

1. In an interior wall behind bathroom sinks I hear what sounds like water running.
2. There is no visible leaking anywhere.
3. This has been going on for a couple weeks and the sound seems louder every day.
4. My 1994 house is on a concrete slab in AZ with 2x6 wood-framed walls, no water softener, hard water.
5. No water is running (water meter dials are still).
6. I shut the main valve coming into the house and still hear the sound.
7. But when I shut the main valve and run the faucet to drain the system, the sound stops.

What the heck is going on? Is this a problem beyond the noise irritant? I have a layman's thought or two but I'm not in any way a plumber so won't say it to unduly influence opinions.

Thank you for any help anyone can give to solve this riddle!

House on a slab built in '94 good chance the lines are under the concrete slab.
Small leaks sometimes do not show on meter.
Get a water test gauge and put it on a hose bib.
Turn off main to house. if the valve you turned off works 100% and you do not have any visible leaks at any fixture than the gauge should hold.
To check if your Valve holds 100% with it still off release a little pressure at a faucet from the system so the gauge drops. With every thing off except hose bib with gauge, the gauge should not move. If it starts climbing your main valve leaks by a little. This would explain why you still hear it with the main valve off.

Often people will here the leak resonating in the wall but it is actually under the slab.

95% of them are on the hot system. Try isolating the hot from cold and retest.

Does your A/C condensate drain into the sink drain? It often sounds like water running in the wall, but it shouldn't be something new.

If your A/C or water heater is in the attic, check them for leaks. Their overflow drains may run thru that wall.

An infrared camera might help you pinpoint the source or location of the water intrusion.