<VV> LM Chrome Windshield Header

[Brian]

I am working on bringing back to life a 1965 Corso convertible owned by a woman in our club. She is the original owner. The car has sat for almost 20 years after being painted and having a new top installed. One of the things I had to do was remove the chrome header across the top of the windshield. I don't mean the small stainless trim surrounding the windshield I mean that big chrome or stainless piece that runs from one side to the other.

I had to remove it because I needed to paint the section below it on the inside of the passenger compartment which is normally interior trim color. On this car there was a lot of rust which someone had tried to cover up with some strange looking paint. 

My question is what should be under that chrome header? When I took it off I found two small pieces of thick rubber weatherstripping one on each side but the middle had nothing. I am concerned that in the rain water would be blown up under the header and leak down onto the dashboard. Can anybody tell me what should be there? Should there be some type of black rubber weatherstripping or some of that old gray putty commonly called dum dum.Any help appreciated.Thanks.
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