When you press the brake there are two motions. One is the piston pushing out of the caliper and inner pad into the rotor. The second is the outer part of the caliper sliding into the rotor. This creates a pinch to the rotor. If the slides are dry and or frozen only one side is gripping.
You would see this in the pad wear.
It wouldn’t cause the 2nd pump of the pedal to be solid.
Big thing is why a 2nd pump. First hitting the floor or close may be air, leak, or fluid pushing past piston on master cylinder. But these dont make the 2nd press solid. Crimped line bad booster ir rubber line. Two you would notice when bleeding.
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