Heating & cooling system
For the head gasket, you could do a compression test, you would find a low cylinder or two, check the exhaust to see if there is a lot of white smoke coming out, coolant could get into the oil, check the oil to see if it is milky, the engine could over heat. On the water pump, usually they start leaking, you would see wetness in the area of the water pump or a drip mark on the ground.
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