I haven't read any commentary on this; perhaps someone else has.
The chief fact about Tiresias (in myth) is the rage he engendered in Hera by
judging that women enjoyed sex more than men. For this she struck him blind.
Zeus could not reverse what another god had done but he could add to it, &
to compensate Tiresias for the loss of vision he gave him/her _second
sight_, i.e., the gift of prophecy, of knowing. So Tiresias' wisdom (his
power of prophecy) is ultimately rooted in his judgment of the greater
enjoyment of sex by women.
In other words, when he was a woman he enjoyed sex more than he did when he
was male, and it is that fact which leads to the judgment which leads to his
blindness which leads to his wisdom. It is because women enjoy sex more than
men that Tiresias is able to _see_ (judge) things that others cannot.
He foresses the rape/seduction of the typist (home at from the typing pool
as the sailor is home from the sea), but that scene differs radically from
his/her own experience, does it not? The female Tireisias got more joy than
her lover from their lovemaking. This cannot be said of the typist.
Is this significant? The implication of an allusion to myth in a poem is
always doubtful, for all myths have multiple aspects (and usually exist in a
number of different versions), and it is never wholly clear in a given
allusion to myth which aspects of the 'original' myth is being 'activated'
in the new context. I haven't mentioned the late experiences of Tiresias,
which come to us (primarily) in the form given them by Sophocles (and this
seems to be important for TWL since it the link of Tiresias to Thebes is
specifically mentioned. There he outrages the man (Creon in the first play,
Antigone; Oedipus in the second play). But it is a bit hard to see the
relevance of either to TWL, given the saturation of the latter with sex.
P.S. Lil's husband is going to want a little comfort when he comes home --
sex, and given Lil's attitude we can imagine him achieving a peace that
fails to satisfy, as does the peace at Versailles echoed in the final line
of the poem.