The parking brake has been used regularly at least the last 3 years. The actuator and piston moved freely right from the start. The piston just doesn't stay in place. I wonder if I didn't get the lip seal properly positioned. As long as I'm taking it apart, that'll be an easy check.
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The seal was indeed the problem, it apparently wasn't seated properly. Reseating it and ensuring the actuator screw was fully extended results in a fully working caliper. Making sure the parking brake was loose at the equalizer made attaching the cable and spring easier but still not as straight-forward as I would expect. Thanks guys.