Oxidation doesn't usually look "black"...it's usually just an overall dullness. I can be splotchy looking if you had clearcoat which was optional on '64s. What you may have is rub marks from a tarp that was applied over the top...that usually leaves more of a black mark and the are usually more linear looking.
Both oxidation &/or rub marks would require polishing or some sort of media blasting to remove. If you can post a picture, maybe we can giveyou a more definitive answer.
If you look at my linked website on the bottom of this post, you will see what oxidation looks like in my "Before" section. We didn't have the black rub marks ~