How actual Gyroscopes work
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from https://www.mcico.com/resources/flight-instruments/how-directional-gyros-work "Directional gyros are unaffected by the conditions that compromise a compass. The directional gyro uses a gyroscope that resists change to its position. It’s connected to a compass card, which moves with changes to the aircraft heading and displays the compass rose direction in 5-degree increments. Mechanical friction eventually catches up and will cause the directional gyro to precess.
Normal procedure is to realign the direction indicator once every 10-to-15 minutes during routine in-flight checks. Failure to do this is a common source of navigation errors among new pilots." So the answer is they precess due to mechanical friction, not because the earth is moving, stop posting false information plz, this is why people hate Flat Earth, it exposes their delusions about how reality really works
So mechanical friction increases depending on how close you are to the non-existent equator?
where did i say that, the friction is between the compass and the non rotating gyro
You claimed that the only source of drift is friction within the mechanism. But in reality, the amount of drift will be different depending on whether you're flying east/west or north/south, and it differs depending on your distance from the equator. None of that would be true on a flat Earth.
On a flat Earth, it wouldn't matter where in the world you are, which direction you're flying, or even whether the plane is moving or not. The amount of drift would be the same every time because none of those factors affect the amount of friction within the instrument.