According to Wikipedia of W.B. Yeats' "Sailing to Byzantium" is
a metaphor for a spiritual journey. Yeats explores his thoughts and musings on how immortality, art, and the human spirit may converge. Through the use of various poetic techniques, Yeats's "Sailing to Byzantium" describes the metaphorical journey of a man pursuing his own vision of eternal life as well as his conception of paradise.
The last couplet of the poem is apparently about the afterlife:
Once out of nature I shall never take
My bodily form from any natural thing,
But such a form as Grecian goldsmiths make
Of hammered gold and gold enamelling
To keep a drowsy Emperor awake;
Or set upon a golden bough to sing
To lords and ladies of Byzantium
Of what is past, or passing, or to come.
The story of Aenaeas and the Golden Bough is about him entering the underworld, to meet his late father in Elysium.
So both have a theme involving an eternal afterlife. But Aeneas' golden bough is an offering, a tool to enter the underworld without dying oneself. Yeats' golden bough is where he sits down, possibly in a timeless existence.
Is the "golden bough" a passing reference to the story of Aeneas, to enhance the theme; or is there a deeper symbolism?