Uh, the magnetic field tracking is ridiculously easy to keep track of, unlike inferring temperature and atmospheric composition.
You just check rocks on the ocean floor, the iron hardens in the direction of the dominant magnetic field. They form visible stripes when you measure for it.
22,000 years - that’s close to the length of a magnus annus.
Is there a connection?
Is it known that there was a full reversal? Or was it just a tilt, then the earth starts to tilt back the other way?
Right now, the North Pole points toward Polaris. 5000 years ago it was pointing toward Thuban. 5000 years from now, it will be pointing toward Alderamin.