Here's the text of the necklace of fireballs, p. 398:
NECKLACE OF FIREBALLS
ITEM 5+
Method of Use worn;
Bulk —
Activation Operate Activation; see text
This string of beads can be worn as a necklace or carried in a hand. (Either way, you must invest the item to be able to activate it.) When tied together as a necklace, it appears to be a hemp string with lustrous red beads of various sizes hanging from it. When held in the hand, it appears in its true form: a golden chain with golden spheres attached by fine threads. You can spend an Operate Activation action to detach a sphere from the necklace. You must spend a second Operate Activation action to hurl the sphere up to 70 feet. (This second Operate Activation action has the ranged trait.) Where the sphere lands, it detonates as a fireball (see page 224). Numerous varieties of the necklace of fireballs exist, each with a different Reflex save DC and a combination of spheres that deal different amounts of damage, as listed below. When all the beads are gone, the necklace can no longer be activated.
Okay, so to begin with, you'll need to invest a point of Resonance into the item to use it. Next, you must spend 1 point of Resonance as an Operate Action to detach a sphere from the necklace. Finally, it costs 1 point of Resonance to use a second Operate Action to hurl the sphere at a target.
Where does this item specify how long must pass between the Operate Action to detach a sphere and the Operate Action to hurl the sphere? If a character obtained this item, wouldn't it be logical for them to simply spend a day's downtime detaching every sphere from the necklace and let their resonance refresh the next day? What happens if they hand a sphere to a different character and each party member throws one on their turn?
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Technically, this one is an error in wording. Yes, as worded that would be the most practical way to use the item, turning it into a Marble Bag of Fireballs... but functionally that is as broken as sucking down a Wand of Cure Light Wounds.
On a conceptional level, this is the wand equivalent of a trinket; it's a wand of fireballs that a noncaster can use. There shouldn't be an investment cost, as there is no benefit. A resonance cost should be spent when a sphere is detached, and sphere must be used by your next daily preparation. If I was the DM I might allow reattaching a sphere during your daily preparation, but I'm generous.
The book is full small things like this that if interpreted the way the rules are stated to us just don't work the way they should conception ally... like a bag of holding. It also has an Operate Activation, with no special exclusion to resonance being spent... which rules as written indicates you'd be spending resonance whenever you opened the bag and possible whenever you took something in and out of the bag. Which obviously can't be true; it should either require a daily investment cost of one, or be one of those rare items that has no cost.
So, yeah. Point this out once, have a laugh at how silly such a world would be, and hope fixing it doesn't fall between the cracks.