The water pump is driven by the timing belt. At the back of the water pump at the rear of the engine underneath the intake manifold is an aluminum water pipe that may be corroded. Sometimes a bad translation from Japanese to English in workshop manuals and parts slides call coolant hose (rubber) water pipes.
...or $550 & tuneup $270 (spark plugs, distributor cap, rotor, air filter) done with the dealer.
Timing belt change included water pump, timing belt, and accessory belt replacements.
After they started working...