The Living Force
As a simple argument from a direction other than basic mechanics, the Milankovitch cycles, which are well-known to correlate to precession of the equinoxes (along with two other variations, the Earth's orbital eccentricity and the tilt of the rotational axis wrt the orbital plane) are well-correlated to climate, with other effects such as those of cosmic bombardment superimposed on top of this.Wrong!
The Earth IS a big gyroscope! Its equatorial bulge doesn’t make it different to any other gyroscope. Gyroscopes in free space don't automatically precess their axis in a constant gravitational field.
If it were subjected to a rotational force it would flip over. Obviously, it’s inertia would make the speed of the flip proportional to the strength of the force, but it would flip in a single motion.
It wouldn’t wobble!
(Unless, of course the force causing the Torque was itself oscillating.)
If precession were due to the Sun following a Birkeland current, there is no reason that precession of the equinoxes should correlate to climate.