Unless I'm mistaken, I believe the washer system is heated continuously. I had that same gurgling noise from inside the car. From what I've read it is trapped air inside the heater core that causes the noise. I had a few leaks coming from a heater hose and expansion tank line.

They were very small leaks but nonetheless I lost a bit of coolant over 6 months. The white residue left as the coolant dried was the clue. I tightened up all the connections and then took off the expansion tank cap and ran the engine at 2000 rpm for 5 minutes on a slight incline with the heat on max. This finally stopped that annoying gurgling sound whenever I ran the heat. It was simply air trapped in the coolant system that needed to be bled out. I would pressure test for leaks and then see if you can identify any leaks particularly around heater hoses.

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1989 300CE