having a "blonde moment" when it comes to gyro procession and props

Pitching a clockwise spinning (seen from the cockpit) prop forward will
result in a yaw to the left, pitching it up will result in a right yaw.
Correct so far?

However, why does a yaw to the right cause a pitch up, and a yaw to the left
cause a pitch down? I thought it would be the other way, given that a yaw to
the right means applying a force to the left of the prop disc, which would
result in the precession force being applied 90 degrees later meaning that
it would pitch DOWN. What am I missing?

Thanks in advance.