So, as we know, the Evas inhabit the soul of the Pilot's mother to allow for piloting. This is (basically) what makes a pilot eligible for the job (except for Rei and Unit 00 obviously).
After doing some basic research on wikipedia it is pointed out that Unit 03 and Unit 04 appear to be the only "Male" Evas in the series (implying that the rest are all female). However, Unit 03 is overtaken by an Angel, and Unit 04 is destroyed in an experiment with the implementation of an S2 Engine*.
So my question is kind of a two-parter; does the "gender" of the Eva itself have an effect on the "eligibility" of the Eva itself, in conjunction with the Soul that inhabits it, and as a bonus; has there ever been any evidence of the Father's soul being used (and if so, did this ever have an impact)?
* I realize that these events are not tied to the capability of the Evas themselves, it's likely purely coincidental