Precession and the ecliptic

[jambouk]

Whilst researching for a talk for my local society I've gone down a rabbit hole about precession and the ecliptic. But I need some help to solve a problem.

I get lunisolar precession, where the Earth wobbles around the axis of the ecliptic by 23.4 degrees over 26,000 years or so. I also get that there is obliquity, where the wobble around the axis of the ecliptic varies between 22 degrees and 24.5 degrees over about 40,000 years. But what I am trying to work out, is why the Earth's ecliptic varies overtime. The graph below suggests it varies on a cycle of 71,400 years or so, and its maximal change is about 4 degrees. I know there is planetary precession, the orbit of the Earth around the Sun along the ecliptic being distorted by other solar system bodies, but the value for this is quoted as 1.2 degrees, maybe 2.4 degrees as the vertex angle, which is still some way off the 4 degrees from this plot reportedly produced by Jean Meeus (https://commons.wikimedia.org/wiki/File:Earth's_orbit_-_Variation_of_inclination_en.png#file).

I thought this paper had the answer, but I can't see it unless I'm missing the wood for the trees: https://www.researchgate.net/publication/250008115_Physical_backgrounds_of_Earth's_rotation_revision_of_the_terminology

Any ideas what causes the 4 degree variation in the ecliptic over a 71,4000 year cycle?

Thanks.

James