A inertial guidance system drifts only because its frame of reference changes.
A gyroscope does not precess unless the frame of reference within which it operates moves.
Forget the Foucault Pendulum.
Buy a gyroscope and do the experiment for yourself.
Mount the gyroscope in any orientation on its tripod support. It will still have two, mutually perpendicular axes of free rotation.
Spin up the gyroscope on a stationary table. Observe it for fifteen minutes. It will not precess.
Of course gyros precess without movement of their frame of reference.
Take your gyro, spin it up, mount it so that its spin axis is horizontal and it’s suspended from one end of the axle, and it will rotate about the mount point.
Unfortunately for you, my father worked for a company with the word “Gyroscope” in its name.
And the gyro you reference is just a toy, not suitable for real work.
And why would I “forget the Foucault Pendulum”? Because it demonstrates the earth rotates?
“Pay no attention to the man behind the curtain”.