It has been brought to my attention that I might have made a mistake! I know, shocking.
Perhaps Iliad disclosing perhaps Odyssey? No, quite the opposite! (8)
"rhapsody" IS intact within the clue, but the verb "disclosing" indicates that the hiding was done in "perhaps Iliad". Not such an egregious error, maybe half a lash worth, at most. Adding in "No, quite the opposite" doesn't clearly indicate that the clue should be switched around.
My apologies, Lex. It's dangerous to rely on my memory these days, but if you do make a mistake or two in the future, you've already paid the horrible price.