No the axis does not noticably change, 1 revolution of precesion every 38,000 years.
but the magnetic deviation does change.
Here on the eastern seaboard of Aus the true north Mag. Deviation is steadily
moving east, currently around 10.5deg east,
heading towards a pole shift in our lifetime by looking at the graph over the last 100 years
wow thats exiting
The sun rise is about 1 degree later every day relative to the stars