The cause of hands whizzing round like that is pallet jewels missing. Broken pivots won't allow the movement to drive at all as the gearing geometry goes and teeth lock up.
It's common for the shellac holding in the pallet jewels to break allowing the jewels to fall out. You only need one jewel to drop for the train to free itself and spin wildly. If it's pin pallet then a broken pin has exactly the same effect.
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