Ann, I'm not familiar with the Eagleston Holly, but at our last house we had a nice East Palatka Holly that turned out to be a female tree. I never did figure out where the pollen came from, but there was no male holly tree within sight of it. Random windblown pollen must have been getting to it from somewhere.
I say 'turned out to be' because the folks that owned the house before us were nutcase pruners, and the holly had been pruned into a torpedo shape
when we got there. I grew it out to a nice normal tree shape and it had lots of pretty berries once we stopped pruning it so it could bloom.