Do I understand you correctly, the squealing is always there and goes away when you tap the brakes?

My experience sounds similar - but different. Squealing when just lightly touching the brakes, but only when the weather has been dry. I've had new brakes all around and it still happens so it's not the squealers. I was told the materials in newer pads are harder (no asbestos or something like that) and tend to squeal a lot, but if that were the case we'd be hearing lots of squealing in traffic all the time.

Maybe in your case the pads/calipers haven't released completely and are stuck just barely rubbing (enough to squeal) but increased pressure when you brake makes it stop. If this is the issue (as it was in my case) perhaps lubricating the calipers might release them more. It's notoriously hard to identify what brake or even side might be the culprit, but is one (or more) rotors very hot after normal driving - enough to boil off spit in an instant. Then it probably isn't releasing completely and is in nearly constant contact.

That's my guess anyway.