The speaker in this section does not seem to be the main narrator. The speaker talks of a presence who is felt, if not seen, when the speaker and the spoken to are seperated from each other (line 361.) Indeed we are not sure if the two ever walk together as the other and the mysterious figure do. Left unsaid is whether this figure is the cause of the seperation.
The third appears to be a ghost, its walk described as a glide. The presence is hooded and the speaker cannot tell whether the figure is a man or a woman but Eliot has previously given us a clue. In his note to line 46 Eliot associates the hooded figure with the Hanged God of Frazer. So here we find the hanged man that Madame Sosostris could not see in the Tarot reading (lines 54-55.) What is mysterious to Madame Sosostris and the speaker becomes, with effort, accessible to us.
While the public reading of this section put forth by Eliot and many critics is the resurrected Christ's journey to Emmaus with his disciples (told in The Gospel of Luke, Chapter 24) Eliot's notes cannot always be treated as a final authority on his meaning. His notes to line 46 and to Part V mention Emmaus yet his note to line 360 does not mention Emmaus or Christ at all. This latter note seems to be a clue that that there may be a more private reading possible to this section. James E. Miller, Jr. provides us with one such private meaning involving Jean Verdenal:
James E. Miller, Jr.
It is a safe assumption the Vivienne Eliot learned early in her marriage that she was in some obscure sense competing with someone whose presence was more felt than seen. The passage above is not so shrill as the monologue in "A Game of Chess," [monologue starts at line 111] but there is the same nervousness and puzzlement--and nagging. Most telling, perhaps, is the line, "I do not know whether a man or a woman." [line 364] The silent party in this unequal exchange surely knows, for we have just witnessed his anguish over the incontrovertible fact--"He who was living is now dead." [line 328] The other who is walking by his side is the enduring memory which will not die, a memory as intrusive in a marriage as a physical presence.