There is a simple way to look at the dilemma. Look at what the singular ending -is. It is in Greek an adjectival form, indicating son or daughter of. The genitive singular form becomes '-idis' and the nominative plural becomes '-ides'.
So Peisistratos who became 'tyrant' in Athens 546BCE till his death in 527. The tyranny was maintained by his next two male generations till their overthrow in 510. Collectively, they were known by the clan name of 'Peisistratides (Πεισιστρατιδες)', or the 'Peisistratid clan'. One of them is called a Peisistratis (Πεισιστρατις). But the singular is not often found, because clans are generally and inevitably plural. Historians of ancient Greek history, though, use Peisistratid rather than peisistratis as the true 'base' or 'stem' word. And they use the anglo-saxon '-s' to form the plural.
Clan names come a lot into Greek tragedy, also. The daughters of King Danaus (the Danaides - Δαναιδες), in English Danaids are fleeing from forced marriage to the sons of Aegyptos and come to Argos to plead for (Hiketeuo) refuge to the king Pelasgos. The tetralogy (three tragedies and a satyr play) is called The Danaids - Δαναιδες or Daughters of Danaus. In English this translates to The Danaids, and the one surviving individual tragedy is called Hiketides - Ικετιδες. This usually comes into English as Suppliants or Suppliant Women. Plays at this time were often named for their choruses, which, in this play, consisted of the suppliant daughters of Danaus. Their natural number is plural, not singular: The are a plurality, just like members of a family.
Just as the chorus was a plurality, so, to the ancient watcher of the night sky, constellations were and are by definition pluralities, or, in other words, a sort of 'plural unit'. On the analogy of Peisistratid, one member of the ephemerides would be an ephemerid, but more commonly thought of as one of the ephemerides and one of the Pleiades would be a Pleiad but more naturally as a member of (or just one of) the Pleiades. The Cambridge English dictionary gives 'Pleiades' as the spelling.