Resolved: Caliper seals were hard.

The front brakes on my '09 Cayman are clicking when pressed loud enough to be heard over the radio. The clicking can also be felt in the pedal. The car can be on or off, moving or stationary.
Video file attached below.
This is a series of approximately 5-20 loud clicks both is application of brakes and release of pressure.
The noise comes from both of the the caliper/pads.
Both sides started simultaneously.
I have changed rotors, rattle springs, and pads, cleaned lubricated, with and without various multiple anti-squeal OEM and textar shim types.
Pistons move free and smooth.
Caliper bolts torqued.
Brakes blead multiple times.
Master cylinder feels smooth when bleeding.
All work and parts above were done due to noise. So deflective replacement parks and work are highly unlikely.

I am unable to determine if it is master cylinder, both calipers, ABS block, or other cause. I generally don't guess, but replaced the rotors and pads as they were coming due.