After carefully reading the definition of a magic item in the PRD, and James Risner's reference, I agree with Aureus that the Shaken effect should get a 5 minute duration. From the PRD:
"Caster Level (CL): . . . The caster level determines the item's saving throw bonus, as well as range or other level-dependent aspects of the powers of the item (if variable)."
That strongly suggests to me that when you're not sure about some facet of an item's effect, such as duration, use the caster level as a guide, and the only thing that has a caster level related to this item is Doom.
Moreover I dislike Mr. Risner's reference from the book about the source of the fear. The text on page 563 doesn't clarify how long fear conditions last, but rather how an ongoing fear condition may influence a creature's behavior variably depending on whether or not the source of the fear is present.
Are there many magic items with this kind of vagueness though? Having to suss it out and make intuitive leaps like this is kind of bothersome.