In my opinion we don't focus enough on this passage told by Pausanias. This is HUGE!Odysseus allows Penelope to choose who she prefers to follow, with the distinct possibility that Penelope will choose her father. In fact, in the "son-in-law's marriage" (i.e. the one in which the spouses move to the bride's father's house) the woman's position is much stronger than in the "daughter-in-law's marriage". By following Odysseus, Penelope chooses to abandon her family and will be asked to get used to a series of new habits, customs, even a different dialect.
So basically Odysseus makes a choice we wouldn't expect, Penelope does the same. Maybe it's just my impression, but it seems to me that one of the many things they have in common is doing things that were a little strange for the time. I won't go into this further, but there are many aspects of Odysseus to discuss in these terms, perhaps I will make a dedicated post later.
The veil is, we could say, the symbol that separates Penelope's life as a maiden from her life as wife of Odysseus.
I had also read an interesting comment about Penelope's use of the veil by an Italian scholar, which reads as follows: "Like her husband Odysseus once used to keep his eyes lowered, because he was thinking, and then his gaze would escape everyone; so Penelope, when she went down into the great room, lifted her peplos on the cheeks, so that the minimum of her expression could be seen".
