I took a quick look at the book I referenced and it seems like the statement you made about the last appearance being in 1360 comes from that book. That is right after the "Grey Box", the first product in the Forgotten Realms line was produced. As far as I know, there is no official storyline associated with it since that point in time. This is roughly 130 years before the 'current time' (BG III).
From that book:
The last reported sighting is in the hands of a mysterious female human figure, who strode through the City of the Dead in Waterdeep on a warm, moonlit summer night in 1360 DR. She was clad only in a carnival-mask that encased her entire head in the mock feathered and keen-eyed head of a falcon. Her left leg bore a sinuous blue tattoo, the outline of a slender snake climbing her thigh. She was seen to hold the statuette high as she left the City (by its most southerly gate) so that it caught the moonlight, and she was laughing loudly.
From that I could go a variety of ways if I wanted to capitalize upon the lore.
One option: I could use this as a supplement to Rime of the Frostmaiden. That module ends at level 9, IIRC, and a common ending to it would provide a potential desired use for an artifact of Auril. The PCs might be trying to find the artifact to stop it from being used to bring back something that dies in the module.
As for where it might be found, I would reference clues in the above description of the last sighting of the artifact:
- Scantily clad human female
- Mask with animal motif - falcon
- Snake tattoo
- Headed out the southerly gate
Anhur, a protective and benevolent god in the Mulhorand pantheon, is a god of war and weather. The Falcon was one of his favored animals. Mulhorand was South and East of Waterdeep - and the Southern Most gate of Waterdeep faces South East. This woman could have been a priest of his that sought to contain the power of other Weather Gods that might be used for evil. The priests of Anhur often tattooed themselves to commemorate achievements - and a victory over a faction of Set, who is associated with Serpents, might explain the tattoo.
If the PCs uncover the tale and connect the dots I laid out you might send them to present day Mulhorand and was subsumed by High Imaskar - until the Second Sundering when they were overthrown by descendants of the Mulhorandi gods who were possessed by their ancestors. That was about a decade prior to "present time". The PCs could travel to this recently 'restored' realms and find themselves exploring the lost ruins of the empire destroyed in the Spellplague in order to recover or protect the Auril artifact so that it could not be used to hasten the return of something vile in the Frozen North.
From there you could have a structure of a Dungeon Delve into an Egyptian inspired tomb, an extra planar adventure from a gate found at the heart of the Tomb where the PCs encounter a prophecy detailing how the statue was disassembled and sent to three locations, and then adventures to collect or protect the pieces from three locations. You might go with a twist where an ally working with the PCs is replaced by a Doppelganger (or was a traitor all along) and have a potential resolution to the Storyline be battling the the thing that is trying to return (either after a return or on another plane where it is banished in order to contain it there).