Matthew Parsons presented some cogent arguments about precession.
Some proofs for your consideration that the blade is bouncing up and down, and not precessing:
The blade changes its gamma based on its inertia, its flapping hinge geometry, its forward speed, its hinge offset and its aerodynamic damping. We can make major changes to the phase of the rotor with these terms. We can even change gamma by putting a weight somewhere on the span of the blade!
A gyroscope changes its 90 degree precession angle only if you move it to the Bizarro Universe, where there is another Law of Conservation of Angular Momentum. If someone can show me a Gyroscope that changes its precession angle, I'm listening.
The equations of motion of the rotor blade flap behavior contain terms for the rotational speed, and certainly account for the change in CF as the principle term that automatically "retunes" the blade to resonate at 1 per rev. It is the dynamic response of the blade's flapping as opposed by the restoring CF that makes it resonate. No CF, no resonance.
The Bifilar pendulum absorbers on many Sikorsky rotors (and inside many older recip engines) is a lag resonant device that behaves exactly as the rotor blade does, except it does it in the in-plane direction. It also self tunes to the operating rpm of the rotor.