Either Jane or Mary was at home.

Either Jane or Mary were at home.

May I ask which of those is correct? Thank you very much!

With a compound "or" subject (like Either Jane or Mary), make the verb agree with the subject that comes second. In this case, they are both single subjects, but let's say it was "Either Mary or the boys were home" or "Either the boys or Mary was home."
Thank you, Barbara. That's a very detailed explanation. I got even more than I expected.