I had a similar thing end up being rust that got behind the dust shield. You prob have something inside the rotor/drum or between dust shield and rotor.

If you remove the rotor I bet you'll find a spot where the rust is evidently scraped away.

I hear a double tap that might show up as two high spots on the rotor.

Since it goes away faster it can also be on the outer edge of the rotor; as the rotor wears, sometimes the lip that grows on the end can touch parts of the caliper. Look for a scrape evidence.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)