Homeric chronology doesn't admit any kind of strict chronology and it will always collapse under the pressure if you try to make it stick to a regulated number of days, with different actions matching up against each other on the correct day, like you get in The Lord of the Rings.

An audience's perception of time always matters more than strict chronology. Perception of time, or sometimes chronology in its immediate local context. Oliver Taplin, Homeric soundings (1992) 15-18, for example, counts 'narrated days' of action: the period of 11 days of plague in book 1 doesn't 'count' because it's not narrated. It's using this kind of approach that, for example, we get one council of the gods in Odyssey book 1, then apparently the same council again (but following a different character at the end) in book 5, when according to a strict chronology they should be three weeks apart; or Telemachus apparently spending a month in Sparta sitting on his thumb from the end of Odyssey book 4 until book 15.

It makes no difference whether we go with the literalist chronology or a relative chronology, as it happens, because it comes out the same way either way. It's two days. On day 0 Hector defeats Patroclus and the body is brought back to the Greek camp; then we have a night, starting somewhere in the middle of Iliad book 18; day 1 dawns at the first line of book 19, and the following day is Achilles' aristeia; nightfall comes near the start of book 23 and we get the bit with Patroclus' ghost; and then day 2 is the funeral games and Patroclus' cremation.

Taplin thinks the Iliad is structured around 'narrated days' -- so books 11 to 18 are all a single day, and he therefore thinks they constitute a coherent conceptual chunk. Maybe. I don't have a huge amount of faith in that to be honest.

My feeling is that the scale of days is so warped, and subject to whatever happens to be going on at the moment, that I think it just boils down to narratological perception -- if it feels like time for a narrative break, we might as well have nightfall. A given number of lines could represent any number of days, depending on what the poet wants.

The Odyssey's treatment of Telemachus' sojourn in Sparta would be a potent counterargument to that though. There, half the Odyssey passes by, but in book 15 it seems like Telemachus has only been there overnight. Well, maybe. Ultimately what it comes down to is something I think Taplin and I would agree on, that the treatment of how much time passes is always open to the narrator's discretion -- that Homer exercises 'artful control of narrative-time' (p. 15).