Determine source of difference between Kapteyn and PyAST for FK4/FK5

For the FK4 <-> FK5 conversion, there is a disagreement of 4mas between PyAST and Kapteyn. Pyephem is worse, but for now I'm interested in understanding the difference between PyAST and Kapteyn, because I can locally get astropy to agree with kapteyn to machine precision (almost) but it therefore disagrees with PyAST by ~4mas.

I think both PyAST and Kapteyn are correctly assuming the epoch of observation is J2000. What else could be the source of the difference? @timj and @dsberry - do you have any ideas? Kapteyn is including the e-terms for FK4 - is that also the case for PyAST?

I wanted to check if it's to do with the calculation of the e-terms - how do we _not_ include the e-terms in PyAST if they are included by default?