Yes another thing to do in a pad swap, if you aren't going to remove/clean the caliper pistons and the bores. Yes to watching the pads move slightly with pressure. If you can't see that, you likely need to remove the caliper and remove the pistons, and give everything a good sanding. If there are visible deposits, I'll use a brass bristle wheel on the pistons, and the same in a Dremel for the bores. Wear eye protection for the Dremel. A mechanic's bib is a good thing to prevent you from becoming a human pincushion in the chest and arms from errant flying bristles. Harbor Freight has packages of assorted brass Dremel-style wheels.
A tip for the smallest one which resembles a paintbrush: use a piece of heat-shrink tubing and place it halfway-up the bristles. The brass brush will work in nooks and crannies like the bottom corner of a caliper, or the corners of a master cyl. better, w/o spreading-out.
View attachment 91173
I like Weiler wire wheels, they have better balance, and seem to stay together better. They are more-expensive.
Power Mini Brushes | Weiler Abrasives
The product catalog:
Power Brushes | Weiler Abrasives
This is the $10 HFT 8" brass wheel.
- 1-1/4 in., 1 in., 7/8 in., 3/4 in., 5/8 in., 1/2 in. arbor with ten inserts for most grinders: 1 in., 7/8 in., 3/4 in., 5/8 in. and 1/2 in.
- 4500 RPM maximum speed
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https://www.harborfreight.com/8-inch-crimped-brass-wire-wheel-93467.html
They have a 6" wheel too, 5/8" arbor w/a 1/2" adaptor.
For these, I recommend a full-face NIOSH/OSHA rated faceshield.