The crank pulley drives the water pump by a conventional type pulley belt that also rotates the radiator-cooling fan, not the timing belt. It’s not that difficult to change the pump probably 1 hrs work if that. Price for a new Toyota pump is $194 .00 but you can buy a non-Toyota pump for $67.00. (Converted from GB pounds if purchased in the UK) The only thing that could happen when driving through deep water is the drive belt to the pump would start slipping due to getting wet, but that wouldn’t cause it to leak. The only thing I can think of is that the pump you had fitted wasn’t a new one and the internal seals have started to wear or it wasn’t fitted correctly and the gasket needs to be replace, depends where its leaking from. The pumps are normally very reliable the only part that wears is the impellors due to high mileage.
pic`s below to give you some idea of what's inside.
Inserted