Water pump or hose? Thoughts.

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I have a coolant leak at the bottom of water pump/hose. I have removed the passenger side wheel and skirt; lifted the vehicle to gain access to see where the leak is originating. Started the car and no leak. The leaking begins once the thermostat opens. Because of the location and the remaining components in place I could not get my eyes on the source of the leak so I am thinking that the leak is from the hose and not the pump. What say you? Hose or pump. Thanks.