Thank you for the photos of the backmarks. Although they are heavily encrusted/corroded, I can see enough in the New York State Militia button's backmark to be able to tell you it says:
*&* STEELE *&* JOHNSON
That dates it to the 1850s/60s.
I cannot make out enough of the other button's backmark to tell you the name on it. In your photo, I see an indented star at 6 o'clock, the continuing clockwise, an O, and S, then a blank area, then an R (with unreadable ones in between those letters). I think I also see an N (or maybe M) to the right of the star (at approximately 5:30 on a clockface).
Since you can examine the backmark in real-life, please do your best to tell us all of the letters you can make out. Please use a dash for unreadable letters, and an underscore for a blank space.
Example:
*_ ---O-S_-_----R-----
It might say BROOKS BROTHERS * NEW YORK *