My wife's 66 coupe had a similar problem. When the windshield was put in, the installer/owner of the company didn't seal the new rubber gasket in properly. If there is any area in that gasket that is not sealed properly, water will seep in and drip. My wife's car was dripping from the mirror. Water can get between the gasket and the metal and run a ways before it exits inside the car, so you might spend some time looking. Since her paint is not in the best shape, I used a little clear silicon between the metal trim and the rubber, and also between the trim and the paint just around the top. If your paint is in great shape, I'd opt for another approach like possibly trying to find the original putty that was used to seal the trim around the window which I believe RV mechanics still use under corner trim on travel trailers and motor homes. Its a grey putty type substance.