That's a very good question.
It seems it was 1970 or 71 that right side mirrors became standard on all new cars. Through the 1960's there were very few of these, and your car is a lot more authentic without a passenger mirror than with one.
However I believe they WERE available, as an extra cost option. What they looked like on the 64, I don't really know.
My 64 had aftermarket mirrors o it when I got it. Somebody gave me a good mirror for the driver's side, but it happens to be a 65 type. Now -- the nit-picker concours people might pick up on this, but it's actually tough to judge, because 65 mirrors were indeed installed on some 64 models. I think they were all landaus and convertibles. My hardtop might be considered incorrect because of the 65 mirror. But heck -- I'll take it. You can also buy the 65 mirror for the right side, so I can buy a matching one if I want.
The 64 has a rectangular mirror with a long stem. The 65 has a rectangular mirror with a bird emblem on it.