Simius....
Thanks for your information. Very interesting to learn this. I followed your search terms and found some websites with some most interesting button information and photos. None of the sites showed this particular button however. That would have been real serendipity!
Do you think that my reading of the fancy script in the center is really "F W" and if so is there anyone else besides Frederich Wilhelm who could have these initials while also being a member of the Order of the Garter and living in Germany, or having this coat made there?
I do not know, but it somehow seems odd that he would have livery servants involved wearing buttons of the Order. It seems like he would have had more important things and awards on his mind, unless this uniform dates to his youthful years immediately after receiving the award.
Additionally, if this was a servant's uniform it seems odd that this person would wear a breast star. Somehow it is difficult to put this all together. Any thoughts?