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I also found the fan to be loose. Seems to be the fan clutch, not the water pump. Anyone ever hear of them coming apart while driving?
Do you mean the small shaft has slop going to the clutch? If so your clutch is getting worn and yes they are known to come apart. If that happens you'll be buying a new radiator, fan shroud and anything else it decides to destroy. Our local EMT's always replace the fan clutch whenever the radiator is replaced.