Literally it seems to mean: that which is not due to anything, or more simply, the causeless, seeing as 'ἕνεκα’ is often translated as ‘on account of’ or ‘due to’. I would think this would be a better term for the first cause, not the final cause.
I have another idea. Maybe it would be better translated as ‘the unaccounted for’. So suppose being alive is what one would call a final cause. Why live? My desire to learn greek is because it is fun, but my desire for life isn’t because of something else, it is unaccounted for.
Rough breathing. It’s the relative, not the negative.
so would that be “the of which is accounted for”.
No. Try looking up examples of οὗ ἕνεκα alone in Plato and Xenophon. It doesn’t mean “accounted for”. It means “because of which” or similar.