On my 1995 Ram Magnum 5.9 V8
I have heard
"running water noises"
from the passenger side of the dash
each time i have changed coolant.

It has happened with
50/50 antifreeze mix
straight water
and Evans NPG coolant, which is about as viscous as maple syrup.

I have been able to get rid of the water running like noise by parking the truck on a steep uphill and running the fully warmed up engine at 1500 RPM for ten to twenty minutes.

It is interesting to know that a vacuum filling technique helps on coolant. Vacuum filling certainly seems to help on brake fluid fills.

I know I presently have a slow coolant weep on the upper driver side corner of the timing cover gasket.
I suspect this is one source of air getting in the coolant system.

Small coolant leaks at the timing cover gasket corners seems to be common on older Magnum V8s.