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That looks to be the caliper guide pin and it will move when the brakes are apart like that. If one side doesn't then it is stuck. Good time to change them if he has time. He can check with Gene at gmpartshouse and get a new set or maybe even check with local Advance Auto or Autozone stores.
BOTH of those pins need to move freely for the brakes to operate properly. They are called sliders. If one is stuck, you can probably use a pair of channel locks to work it loose by twisting back and forth. If it is really stuck, use some heat- a propane torch or similar to help loosen it up for removal. Apply heat to the body of the bracket in the area that the pin moves in. Use some solvent to clean both before reinstalling. Use high temp silicone lube - available at any auto parts store - to lube pins and bores. They should slide in and out easily.