Today I tried searching for information on it for the first time in years. The information isn't fully clear, but apparently the authorship of the piece is itself dubious.
One page lists it as WoO. 15, but other sources assign that number to a set of six Ländler. The piece could be considered a Ländler, so maybe it's one of the set. I think of it as a minuet, and others have called it a waltz. In Beethoven's time the waltz and Ländler hadn't clearly separated.
Digging further I found this on Google Books:
It is very possible that the Beethoven piece received its title through a mistake in translation. The work appeared first in 1838, in an edition of a Berlin publisher named Crantz. It was then entitled "Glaube, Liebe, und Hoffnung. Abschiedsgedanken. Walzer für Pianoforte." This means "Faith, Love, and Hope, Parting Thoughts. Waltz for Piano." It is a rather long title for a simple work, but perhaps the "Parting Thoughts" of Crantz were changed into "Farewell," and later on into the present title.
I don't know if anyone else cares, but I'm glad to finally have learned that much.