"we cannot find any text where person A is called the "head'' of person or persons B, and is not in a position of authority over that person or persons"Ptolemy was called the head of the Ptolemies, but was not the authority over his father or other kings in his famiy line. In fact, the only person who was ever called the kephale of a family, tribe or nation of which he was the leader, was Jephthah.
I am not going to change my story on this.
If you want to talk about who is the "head of the household" then you have to go to another Greek phrase oikodespotes. In the verb form, this word is applied to women in 1 Tim. 5:14. In the New Testament, it appears that there were at least a few women who were the head of their own household - Lydia, Chloe, Nympha, the elect lady, and so on.
Any woman reading this needs to know that believing that the husband is the authority in the marriage, has no benefit in terms of getting into heaven, raising one's children well, bringing honour to God, or preventing divorce. Submission to an unpleasant spouse, either husband or wife, may seem to work in the short term, but it is highly dysfunctional in terms of maintaining a relationship, and is in fact, one predictor of divorce. People need to know the truth.