His eygs
His eyes / eggs.
Eggs are everywhere in Finnegans Wake and are symbolic of resurrection; from Humpty Dumpty to "Haroun Childeric Eggeberth" HCE as an egg represents his incubation within his own sleeping body – where, in the morning he "Hatches Cocks' Eggs" and have "iggs" for breakfast "sunny side up with care".
"eygs" suggests both eyes and eggs. There are many physical similarities between eggs and eyes; from their shape, consistency and iris-like appearance when cracked open. The shell is also reminiscent of the eye-lid, keeping the soft, white glutinous ball inside whilst asleep. His eyes are like eggs because they too are in a state of incubation whilst he is sleeping. In the morning ("sunny side up") they will hatch when he wakes and opens his eyes.