One thing to keep in mind: the zero point of the Equation of Time is *not* arbitrary, but comes from the shape of the analemma (or equivalently from the shape of the earth's orbit and orientation of its north pole).
The Equation of Time is the difference between apparent solar time (tied to the sun's right ascension, i.e. its position measured in the earth's equatorial system) and mean solar time (a uniform time scale chosen so that the average is correct). From the definition of mean solar time, the integral of the E. of T. over a year must be zero. That determines its zero point. I haven't checked this, but I'll bet the fact that the zero points of the equation of time lie near the solstices comes from the fact that the peri-/aphelion points of the earth's orbit lie (currently) near the solstice points. That is, the Earth-Sun system is almost symmetrical about the Dec 21 - June 21 axis, and so the analemma has nearly bilateral symmetry about its vertical axis. After a few thousand years of precession of the earth's pole, that won't be close to true, and the analemma's zero points will be displaced a bit further from its bottom and top.
