Where is the drip that you see?
What does an intake valve have to do with a leaky coolant? I could see maybe the hose, maybe the water pump leaks, maybe it does not, but what it does do is circulate the coolant throughout the engine once the thermostat has opened up to allow coolant to circulate.
SO , like you, I remain skeptical that all these things have gone bad.
If I were you, I might consider changing the HOSE, see where the water pump is located and if ya can get to it they are not hard to change. A few screws and a gasket. That's it.
You could remove the radiator and take it to a radiator shop and have them test it and recore it if needed. They are not hard to remove or replace.
Save yourself some big money....
micro...
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