Mine does that too.  Standard brakes.  It only does it when hot though.  I get multiple clicks and clunks though, and a squeal when turning whilst braking at slow speeds.
It probably is pad movement as you've already said, but it shouldn't cause noises like that.    I think in my case the whole lot is just knackered because I also get an inconsistent pedal.  Sometimes uber sharp bite, sometimes not.  Past experience points that to worn calipers/carriers, so I might just replace all of it tbh.  Standard 312s can't be that much?