Reveal

Zeus-nourished son of Laërtes, resourceful Odysseus, reveal your scheme to your son now, and don't hold back.

Odyssey Book 16 line 163-164 Barry B Powell
Odyssey Book 16 line 168-172 Barry B Powell
Odyssey Book 16 line 435-437 Barry B Powell

Odysseus and Athena

and then Athena touched him with her golden wand. First she put a well-washed cloak and a shirt around his chest, and she made him tall and youthful. Once again he grew suntanned and his cheeks filled out, and the beard around his chin grew dark.

But Athena, standing nearby, struck Odysseus the son of Laërtes with her wand and made him again an old man, ....

With Eumaios safely out of the way, Athena signals to Odysseus with her brows and he steps outside the enclosure, where 'Athena' says to him:

Odysseus takes the opportunity to disclose his identity to his son, while the other herders have left with their pigs.

Odysseus cleans himself up, puts on the clothes he's kept hidden from Eumaios and reveals himself, though later on, when Eumaios returns in the evening, by the same magic Odysseus has been transformed again.

You want to know what I think about this? I can only conclude Odysseus doesn't want Eumaios to know about his identity just yet.