John : In looking a little deeper, I found that on the Vintage Thunderbird Club International Forum, they note that the Brown Solenoid is correct for 1961-63 Thunderbirds. I would guess that this would be correct for all 61-63 Ford Models. In addition, they note that the Starter solenoids through 1963 had the FoMoCo script within the "Ford oval", and that sometime in late 1964, this changed to within a rectangle. They do not note when the change from Brown to Black occurred, at least in the Forum, but it is probably in their "Official Factory Specifications" Manual for 1964-66 Thunderbirds, which I do not have.
I also looked at all of the pictures of 1964 Mustangs in our "Unrestored Picture" Section, and, after zooming in to each picture, all appear to be Black. If this is true, then one could say that the change from Brown to Black occurred sometime between the end of 1963, and April of 1964.
Bob