What causes the precession of the earth's axis? What causes this torque? Why is it a 26,000 year cycle? What force in the solar system causes this?

Earth-Moon and Earth-Sun distances change between respective mini-max limits that also change, over centuries. So is the inclination of the Moon/s orbital plane to the Earth's orbital plane.

Almost-periodic #mu#-level changes in magnitude and direction of the forces of attraction on the Earth, from nearby small Moon and far away big Sun cause cause axial--precession and also nutation..

Despite the Sun is far away, its mass is about 330000 X Earth's The effect of Sun's force is complimentary to the force from the nearby Moon. Lunar orbital period is less than a month and its motion includes regression of going behind the Earth for alternate fortnights..The combined effect is revealed in periodic tides in river mouths, bays and estuaries.

In a similar way, the Earth, as a whole body, responds to these changes through precession of Earth axis that is periodic over a great period of about 260 centuries. The poles move in an oscillatory manner about respective circles, described in this Great Year of 260 centuries. Nutation (nodding) refers to these small oscillations that are of different small periods that are compounded into a single period of Great Year.

Evidence for precession is the shift of equinox location on the equator, by about 820 meters every year..