Eldership is conditional and there are prerequisites. One of those prerequisites is being a
man. What constitutes a qualified man, among other things, is what follows:
Titus 1
5The reason I left you in Crete was that you might put in order what was left unfinished and appoint elders in every town, as I directed you.
6An elder must be
blameless,
faithful to his wife, a
man whose
children believe and are not open to the charge of being wild and disobedient.
7Since an overseer manages God’s household, he must be
blameless—
not overbearing, not
quick-tempered, not given to
drunkenness, not
violent, not pursuing
dishonest gain.
8Rather, he must be
hospitable, one who
loves what is good, who is
self-controlled,
upright,
holy and
disciplined.
9He must
hold firmly to the trustworthy message as it has been taught, so that he can
encourage others by sound doctrine and refute those who oppose it.
In the rare event there are no men available, who have the above characteristics and qualifications, then they aren't the kind of men Paul said a woman can't have authority over. Hence why it wouldn't be a violation for a woman to oversee unqualified men of these types.
So my questions for your claims are, where is a woman completely forbidden from being an elder? In the event my "rare situation" occurred, is it better to leave the congregation without an overseer of God's household?