What is the meaning of "Docile pitch behavior" in the context of Pugachev's Cobra?
"Docile" means no big pitching moments over the angle of attack range. Since the control power with fully stalled control surfaces is rather small, the airframe must not create strong pitching moments, but keep a small pitch-down moment so the airplane returns eventually to normal angles of attack which allow regular flight.

The maneuver is dynamic, so the pilot needs to build up a specific pitch rate. Inertia will keep the aircraft pitching up, and the small pitch-down moment (and aerodynamic damping) will reduce the pitch rate so that the pitch-up stops when the nose is pointing straight up. What follows is the consequence of the small pitch-down moment: The aircraft slowly returns to controlled flight, and once control authority is re-established, the pilot stops the pitching motion.

By selecting the initial pitch rate, the pilot can control the maximum angle of attack, but once he leaves the flight regime of attached flow, he has to wait until inertia and aerodynamics do their part.