Not sure if this counts, but I hope before I die they find even one more of the poems from the Epic Cycle. Particularly The Telegony (sequel to The Odyssey), The Aithiopis (sequel to The Iliad where Achilles dies), or The Little Iliad (sequel to The Aithiopis where they build the Trojan Horse).
What's your personal great white whale of an unsolved mystery? The thing you desperately hope is solved before you die because you need to know the answer? Mine is the Isabella Stewart Gardener Museum heist. Where the hell are the Rembrandts. I need the full story