Re: Eimear- AY-ver or AY-mer
Éimhear, Eimear and Eamhair are cognates of Emer (EE-mer) and you do find Éimhear more commonly on girls here in the UK (though it's still a rare name, Emer is more popular)
Éibhear is a male name, according to legend the son of Míl, leader of the first Gaels to settle in Ireland. Perhaps that will help?
Devon