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Archmage Vargoth's Spare Staff is looted from  Mysterious Shining Lockbox.  The lockbox is already unlocked, so there is no need to find a rogue to lockpick it.  The lockbox itself is a reward from a Rare garrison mission called Finding Farahlon.

The staff is a nod to the many players who held on to  Archmage Vargoth's Staff after completing the quest it was provided for.

If you ever want to visit the archmage in the flesh, you'll need to complete the achievement  Higher Learning which awards  The Schools of Arcane Magic - Mastery.  This is the only means of entering Vargoth's room in Dalaran.

The Toy Box allows players to store vanity items in a manner similar to companions and mounts, without requiring physical storage space. The Toy Box is accessible through the user interface, as part of what is currently the Mounts And Pets interface.  The Toy Box is account wide, so you will only need to acquire the staff on one character.

Note:  This item, oddly, is not displayed in the default Toy Box user interface; you'll only see it if you have learned it.