No you shouldnt hear water trickling, if your talking about the box on the passenger side it may be hot after driving for awhile. Im not 100% sure but I belive that your heater core is on the other side of that. It may be leaking and in need of being replaced. Get a pressure tester and do a pressure test on your cooling system. You can rent one at autozone for liek 80$ and when you bring it back you get all that money back broken or not. (I know I work there). But you shouldnt hear anything trickling there so it might be leaking. Do you see anything leaking anywhere or smell antifreeze?
Sounds like your heater core sprung a leak. Easy way to check, is to check what fluid is coming out of your HVAC drain tube, which is where the water drains when you run the AC, if you see radiator fluid coming of it, then life is going to get very difficult. You'll need a new heater core, and about 6-12 hours of spare time to replace it.
Really pretty easy the bottom of the box comes off can probably do in 1-2 hours, If its like the one in my suburban. Take 2 screws out of bottom right side of box, pull down a little, if antifreeze comes out there u go. There is about 6 screws altogether on bottom of box. Make sure u get the one on the back of the box. You cant see it but you can feel it. Good luck
The thing that has me stumped is that whenever I fill it up now it seems to drop to the same spot. I have yet to see a puddle of antifreeze on the ground or had any in the cab. It may sort of smell in the cab, but I don't know if that is just from sitting awhile.
I had a similar problem with my 97 silverado, i was loosing coolant, the first thing i checked was the heater core, because in this model is really easy to check. Then i checked the radiator and the water pump, but i still had coolant loss, so i checked the oil cap, oh big surprise i had water drops in top of the oil cap, so at that point i knew it was the intake manifold gasket, in this model the intake manifold gasket is more likely to fail than the water pump. to replace it wook 2-3 labor hours and 25 dlls gasket pack at autozone.
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