If that is the case probably a case of old age.The pump, not the driver!
Do the seatbelts and "goggles" look any better now ? The Cooper, which is usually very reliable disgraced itself in New Zealand last month with DNF's in nearly every race due to overheating, suspect the water pump has lost its impellor blades. Is this a common Climax ailment ?
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Though basics, has the radiator blocked itself up?
Sad to go that far on to what seems some great tracks and have problems.