You might want to consider spending the 40 bux to get a cowl vent cover to keep in the car just in case you get caught out in the rain, or you want to run it through a car wash.
http://www.canadianmustang.com/store.mv?p=802335-802336

 

Pain in the *ss but you should check your cowl inlets under the dash - one on the drivers side has the fresh air vent attached, passenger side you will need to remove the heater box (good time to check the heater core to see if it or hose connections are leaking, especially since you say the rot is worse on that side) Run some water into the cowl in front of the windshield and see if the cowl inlets into the car are leaking (they have round inner pieces up inside the cowl that is supposed to keep the water from going inside the car - this is where they usually leak) If it is just a small to medium leak around the round opening into the cowl, get yourself some cowl repair inserts and RTV them in there - should have no more leak. Cowl inserts look like top hats with the top cut out, small investment, big fix and readily available from most any Classic Mustang parts vendor.

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