My guess is that the visor is only available as a unit. It is unlikely that you will find one being parted out by a used parts place. A visor is much easier to sell as a complete unit. A dealership can tell you for sure how the part is available.
Another alternative that is not a good one is that you could glue the cover closed to ensure that the light stays off and your battery does not get drained. That would hold you over until you could find what you are looking for. Perhaps you could buy an ugly but complete visor at a Vette show to get the parts you need.