Water in heater box on a 1999 Dodge Ram 1500 4X4 Quad cab. I can hear water rushing around in the dashboard but have no visible leaks

In regards to the swishing water. Had the same problem on my 99 Jimmy. Reason for the problem was air pockets due to low coolant level in my rad and any empty reserve tank. Drained rad and refilled till absolutlely full. Filled reserve tank to proper level and waited for thermostat to open and **** in coolant, level goes down. Top it up and repeat till rad level stays full and no air will be present. Bybe bye to swishing water sound. Hope this helps.

Alan,is this only on vihicle start-up and taking off from corners when accelerating,if so,sounds like air in heater core,you could try to purge air out with a manual system pressure tester or run vehicle from cold start with rad cap off for 15 minutes at 1200 rpm to purge air from system,also dont rule out basics,verify rain water drain ports are clear and not plugged

Make sure the drain is clear, it in engine compartment agaist fire wall were heater box is located.