When I bought my '65, it had the run-on problem. It was caused by an over-rich condition causing carbon buildup in the combustion chambers, mostly the piston tops. When the car was shut down, the carbon was still hot, and the compression very high, causing the engine to run-on (like a deisel).
The temporary cure was to advance the timing (turn the distributor clockwise). Ultimately I had to implement a combination of smaller jet sizes, timing using a vacuum guage, and getting the Holley adjustment screws to function at idle (this last feat was accomplished by pulling the Holley, and replacing it with an Edelbrock. I couldn't bring myself to drill holes in it).