These passages are taken from 'Appendix II - λυκάβαντος: when the wolf comes?' in Elisabeth Irwin's 'Solon and Early Greek Poetry: The Politics of Exhortation'.
At Odyssey 14.158–64 and 19.303–7, the disguised Odysseus swears oaths, amounting to prophecy, to Eumaeus and to Penelope, respectively, that Odysseus’ return is imminent.
These passages are famous for the controversy surrounding the meaning of the critical phrase τοῦδ' αὐτοῦ λυκάβαντος: λυκάβας is a term otherwise unattested in Homer and one that does not resurface until some few centuries later, glossed by the less enigmatic term, 'year'.
None of the arguments proposed for the ‘true’ etymology are fully convincing: the origins of λυκάβας are alternatively proposed as pre-Greek—quite possibly related to the prehellenic name of the Attic mountain λυκαβηττός—or even Semitic. The first half of the word has been alternatively derived from 'light' or 'wolf', and the second from βαίνω ('to walk') so rendering the phrase 'when the wolf walks' or 'when the light goes'.
Here one might return to the phrase itself, and not its disputed etymology, but its possible folk etymologies. For the scholiasts the association of the word with year came from a connection with the wolf, λύκος, which they justified by the supposed amazing cooperative power of wolves who, each grasping in their jaws the tail of the wolf in front, were said to form a chain to cross rivers, a sequence that is said to evoke the motion of time as sequential units (ὥσπερ καἰ ἐπὶ τοῦ χρόνου, 'as also in the case of time'). The explanation is fanciful, but at least points to a tradition of associating the word more distinctly with 'wolf' rather than 'light'.