on most non hybrid vehicles the water pump is driven by a V belt or serpentine belt, as are the AC compressor, power steering, alternator. None that I know of are driven by the timing chain.Timing belts don't stretch, timing chains do.
That being said, I am always wondering the longevity of other components in the chain, like tensioners or idler pulley etc. Do they last a lifetime? Also water pump. Do they move water pump to drive belt when using chains? Thanks
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Timing chain vehicles in general have a hydraulic chain tensioner to apply a slight amount of pressure to keep the chain under mild tension.
there are a few vehicles where the water pump is gear driven off the crankshaft, the ones I'm aware of are all diesels, the GM duramax is one with a gear drive water pump. I suspect one reason is to reduce side load on the pump shaft from a serpentine belt to increase water pump life. On the duramax diesel water pump replacement is extremely rare, even on vehicles approaching 300K-500K+ miles.
On newer non hybrid vehicles there seems to be a migration to electric drive for power steering, probably to increase fuel mileage. Most/all hybrids have gone to electric drive for water pump, AC, power steering and brake booster. Our MDX hybrid is one such vehicle.