The shock towers are flexing from age and miles. Install a Monte Carlo Bar between the shock towers and that should do it. They are available from any Mustang resto parts dealer.
They come in straight or curved, black paint or chrome. The curved gives a bit more room at the distributor on V8 engines. They mount with bolts and attach at the upper inner fenders, just in front of the shock towers. You may need to jack the towers apart a small amount for the bar to be inserted. It's because most of these old horses have settled and the towers have narrowed. This is an old Shelby trick and it will give the front end rigidity plus better handling, as well as getting rid of the cowl shake.
They don't cost much, around $20 for the painted and $30 for the chrome. I wouldn't have an old pony without one. | 
65 Mustang Convertible cowl shake? 
