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My truck doesn't have a cowl vent
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The truck has a hood, firewall, windshield, and wipers and that is what matters. There is the pan area below where the windshield meets the hood and firewall and the area where the wiper motors are, both collect water and if the hose or channel is clogged, the water finds another route IE down the firewall and into the cabs floorboards. Firewalls are not really sealed anymore as there is to much stuff entering and exiting the passenger area. The truck is over twelve years old so the cables have moved and wiggled creating holes and gaps. A cable gasket could have popped out and is hanging on the cable and not plugging the firewall penetration.
Remember water will always follow the path of least resistance. So if the drain or channel is clogged, the water fills up the void like a pond and when the pond can't hold anymore water, the water flows away from the pond taking the path of least resistance. Since the area was meant to trap water then exit it by drain or channel, the truck maker didn't put extra waterproofing or a second catch with a drain below it, hence it flows into the cab if that is the easiest path to follow. Water will hit a cable, hose, vent, whatever, cling/follow it, hit the firewall, and follow the whatever into the cab. Once inside, it runs to the lowest point collecting on the floor boards.
The hard part is if it is following a hose or vent, there will most likely not be a side or front area wet as the water is coming in, the hose or vent turns up once inside the cab and the water is free falling to the floorboard, not running down the inside firewall. If you are lucky, you can feel above the floorboard up under the dash and feel where its wet then the water is coming in about that. My neighbor found his leak by using a home inspectors wet home moisture detector.
This also happens often if somebody put extra stereo or radio gear in the truck and was not careful how they came through the firewall.