I'm lost Eric...

"Actually torque tendencies from the tail rotor would translate to the lateral axis, not the vertical axis, affecting the pitch, not yaw"

My line of thinking went like this:

The tail rotor's angular velocity has its axis parallel to the pitch axis.

When the helicopter is yawing, the whole thing (including the tail rotor) has an angular velocity around the yaw axis.

The precession torque is simplified as

T = I W x w or T = L x w

where

W and w are the angular velocity vectors of the tail rotor spinning and the yaw rate.

L is the angular momentum of the tail tail rotor (= IW).

I is the moment of inertia of the tail rotor

T is the torque vector due to precession.

x is the vector cross-product symbol.

The precession torque axis is at right angles to the two angular velocities' axes, i.e. the roll axis.

My comment re translation was meant to show that the tail rotor must experience a vertical angular velocity, otherwise it would not be yawing, not that I was seeing things happen while flying sideways.

I agree that there may be forces due to airflow not hitting the tail rotor exactly parallel to its axis, and that I didn't consider them. These forces may dominate any gyroscopic precession at the tail rotor.

You could also expect some roll effects if the tail rotor thrust is not directly in line with the center of mass.