“We could make the noise stop every time by braking …”
If that is the case, the sound is not coming from the “brake pad low” warning indicators. The “low warning indictor tabs” rub against the rotors especially when the brakes are applied.
I suspect the sound is from vibrating shim plates.
If you had your tires rotated, it’s a good chance they lifted your calipers looking for brake wear, and they may have jiggled something. Brake replacements are great money-makers for any shop.