Dobek, I am not an expert here, but we were pulling the chrome moulding that runs around the body at the base of the convertible top and in order to get to some screws, we had to drop down a fiberglass "trough" that follows the car exactly like the moulding and is located in the trunk at the top of the back seat. I am pretty sure this trough is to collect water at the back of the convertible top and run it around to the sides of the car where I think it should drain out somehwere by the rear quarter windows. This is on a '67. Does your car have this trough?
Hopefully, someone can give us more info.