I have been looking to help with this button, also.Really hard to tell wtout a clear pic.Its hard enough wt one.lol
Brokensignal could be right. I really dont know. But the closes I can get from your discription is a british navy button, they date back to 1748 and up. Says same thing about "colour" on back but not exact as yours. Thumbing through book there are several types that say these same things on back ,but none I see that have a eagle wt a shield. Other than british navy. On these Eagles are standing on a mound not a globe.
Although there are some others wt eagles standing on globe in a total different catagory, and they do not have shields or this type of writing on the back.
Another thing that is confusing,, is your button has a date on it.Although there are some buttons that have a date. From what I see there are not many. Is it possible that what you see is not a date but maybe broken letters from a word? Like "EXCESIOR"? Some of these buttons also have other things wrote on them(that could look like a date) and match,somewhat, your disription. They are post revolutionary buttons wt eagle on globe. I am guessing .
Also several categories of buttons say that there are some out there unknown from the 1700's. So who can really knows when the description is so vague.
There are 1000's of buttons so it is really hard to tell ,,,,,,,,,,,,,,,,but I tried. Good Luck
here are some pics out of book of british military buttons and desriptions of them. ( a very small part of what they say and show.