Where, how does water drain from cowl vent??

Front floors both sides are soaked! Dripping wet mats!

Leak first was on passenger side floor only. I suspected heater valve and or core and routed around both. Dried her out and drove for a week, clear weather, it stayed dry inside.

Let car sit for 2 weeks with tarp over roof, all windows, windshield covered.
Cowl vent was UNcovered. rain and then a foot of snow fell, sat, melted. Now floors both side soaked!

I supect cowl vent must be culprit.

Does cowl vent water run down through late model heater box and heater drain tube?

Where's the common leak point? How do you remove cowl vent cover and screen?