Well, given the rarity and elusiveness of Ahab's White Whale, I would have to say there are just a few that fit the bill for me.....they're shotguns and the fact they are all 16 gauge amps up the White Whale factor.
First, I had been dreaming about one day doing a barn find of a Remington 1894 EE grade in 16 gauge. Until 2 years ago, only three were known to exist. Then a guy emailed me with questions about a gun he had just got from some old farmer in a trade for work done. Turns out it's a 1894 16 gauge 2 barrel set. Only 2 barrel EE grade of any gauge known to exist. Value is WELL into the 5 figures USD. A true barn find of just the gun I had imagined!
Then, there would be a Lindner/Charles Daly Diamond in 16 gauge. Sure there are a few out there but I've never seen a picture of one. Most of Lindner's production was for the US market so percentage of 16's would be way lower than a typical German maker from that era.
There would be a W & C Scott Premier in 16 gauge. Never seen one but like the Lindner output, as a London maker, 16's would be few and far between.
And finally would be a Manufrance Ideal 7R/E Ace of Spades in 16 gauge. I've seen a couple come up for auction in France but I don't usually have the 20,000 euros that is the price of admission.
Happily, I'm close with a couple. Have a Lindner/Daly Diamond Quality in 12 gauge along with a very high grade 12 gauge Manufrance Ideal, although it's not an Ace of Spade.
Pretty sure that with $100,000 USD to spend, the Ahab in me could acquire all four whales!