We too had the leak "dripping water from the hood vent". We used to keep a plastic pan under it to catch the water.
I cauked around the hood vent on the exterior and no more drip detected after a few rains. The exterior vent itself looks like two separate parts. There are slots on the vent "snout" on the top and bottom as if it can be snapped off. I didn't try to snap it off to investigate the entire assembly, I just put a nice bead of caulk across the top edge filling in the slots on the upper side to stop water from entering at all.
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