Don't get it in the rain. Well, I guess that's not what you want to here. I have a problem with that on mine. I did seal from the underside where the vent goes up to the cowling area,helped a little bit. They rust out from the top side from water collecting in there . your drains for that area may be plugged up ,mine were. Hard to see with out removing the fenders. I was told by a body shop the only way for a good fix is to remove the top of the cowling and repair it from the top side by welding if its rusted though. More money than i wanted to spend. Maybe somebody else can help both of us with advice.
It sounds like you may have the infamous "cowl rust leak". I have done this repair twice and the worst you are looking at is removing the upper cowl to see what is going on in the lower cowl. What I would suggest is getting on your back and running a flashlight under the dash to see if there any "pinhole leaks". Like mentioned before, water,leaves and crud over years collects around the cowl hat which causes rust to form. I have also found that the section just above the door hinge and below the windshield is notorious for rusting out. Since you already know there is water leaking in there is no need to do the water test. If you plan on taking the upper cowl off using a spot weld cutter it would probably take you about 4 hrs to take it off as there are over 140 spot welds to drill out. If a bodyshop does it for you you are looking at probably between $2k and $3k depending on how bad the cowl is. The cowl is not repopped so you can fab a new piece in including new hats or use the mustang one. However using this method will mean you will need to fab it as the mustang/falcon cowl is different from one another
I ended up having a buddy of mine (auto body guy) re do the cowl on my 63 hardtop. It was a big job but it is like new now. Replacing the bad areas and using using por 15 to coat the inside of the cowl area should make last longer than I will be alive.