What does the "Precession of the Equinoxes" have to do with it? I will buy into the obliquity of the ecliptic, which is changing and which certainly is one of the "astronomical driving functions" of global climate.
I find this:
Since planetary precession due to perturbations from Jupiter and Saturn causes the perihelion of the Earth's orbit to precess, the precession of the Earth's axis relative to the Sun has a period of 21,000-22,000 y.
11,500 is aproximately half of 22,000