Sounds like a me water bubbles ng in my dash

It could be two things.

1. The water drains in the wiper cowl are blocked with leaves, dirt, and debris so you have a pool of water sloshing about in there. You need to remove the collection of debris from around the drain holes of which there are two, one at each end of the cowl.
2. You have air bubbles in the heater core (nothing to do with changing the inverter water pump) and you may even have low coolant in the engine cooling system. Check the level of the radiator directly. You will have to remove the black cover at the front of the engine bay to reveal the radiator filler cap. There should be coolant right up to the top of the radiator filler neck. If you have low coolant you should bleed air out of the system. There are good videos on YouTube and threads here on PC on how to do that.

 

Are you sure it was the inverter pump and not the three way valve? Working on the latter can let air into the engine's coolant system.

For what it's worth, I have only ever heard gurgling noises in a car when there was air in the heater core.

Also possible I suppose if there is a large half filled bottle of water which has rolled under one of the seats. (I keep a liter bottle of water in one of the cup holders in the center console. It sloshes around a little but since it is vertical it doesn't make enough noise to hear it.)