What time value should I use to perform eci2ecef conversions when the axis systems are coincident?

[samuel-emrys]

Hi Team,

This might not be the place for this question, but I'm using pymap3d for this and I'm hoping someone can provide advice - I'm running a simulation that begins at t=0 where the assumption is that at this point ECEF == ECI. As time in the simulation progresses, these two frames naturally deviate. The problem that I'm having is that when using eci2ecef, I'm not sure what datetime value to pass as an argument to replicate this assumption.
The docs indicate that the default assumption is the J2000 frame, which presumably implies t=0 at 2000-01-01 when the earths equatorial plane is coincident with the plane defined by its elliptical orbit around the sun - the vernal equinox. This point is obviously not when ECEF == ECI.
So far I've just attempted to search the solution space iterating over a 24 hour period to identify when norm((R,0,0)_ECI) == norm((R,0,0)_ECEF), which has give me a rough-order-of-magnitude response, but it seems as though eci2ecef only provides a maximum accuracy of 1 second (though it appears it forwards this to astropy, which I assume is capable of providing ~nanosecond accuracy).
I'm wondering if anybody can provide any advice on better ways to identify the time where ECI==ECEF? Is there anything built-in that I'm missing here?