I am re-stating some points here because LouW has asserted more than once that P Factor is a pitching force, not a yawing force. Furthermore, I'm not sure he understands the difference between P Factor and gyroscopic precession. They are different forces, though in some conditions, they have the same result--in others, they tend to cancel each other. In still others, they act in oblique directions to each other.

In a steady state, straight climb, gyroscopic precession is not acting. It only acts while the airplane (actually the rotating propeller) is changing direction (pitch, yaw, or some combination of the two). While pitching toward the canopy, gyroscopic precession responds with a right yaw force. While yawing left, it responds with a pitch up force, and so forth.

The example I gave of a wings-level climb with insufficient rudder, is not a steady-state climb. The airplane will be yawing left slowly, depending mainly on the angle of climb and the power being produced. The heading will be changing slowly to the left. The ball in the turn coordinator will be deflected slightly right. In this case, P Factor (and spiral slipstream) is acting to yaw the airplane left, and gyroscopic precession applies a pitch up force.

If the proper amount of rudder is applied in a wings-level climb, the airplane's heading will be constant and the ball will be centered. This is a steady-state climb and gyroscopic precession is not acting, since the gyro (the propeller and other rotating components, even the alternators!) is not changing orientation.