Hi Paul:
I've not yet found anything for you, sorry.
It's a long story, but when I was about 12 years old we thought we had found a distant Irish relative - names, dates and other facts tied my ancestor (who had an unusual surname) to this lady's "John" who left Ireland in the early 1800's. Several years ago, when I was researching, I found out that my ancestor could not have been our common ancestor. While I do believe my ancestor could be the nephew or cousin of her John (I've yet to find solid proof), we all did make a mistake. I've since learned to never assume anything.
If your James' parents were Hugh Gallagher and Bridget Hanlon, and looking at the New York death record for James Gallagher, I would "assume" that the man who died in 1912 is your great uncle. But, I would try to get more facts before stating he is your relative.
I tried a brief search and did not find anything, but have you tried the following sites:
http://chroniclingamerica.loc.gov/#tab=tab_advanced_search Newspaper search. In the past, I've used general terms when searching. If Mr. Gallagher died in an accident, they may have publishing an article about his death without including his name.
http://www.fultonhistory.com/Fulton.html Newspaper search.
http://www.findagrave.com/cgi-bin/fg.cgi Grave search - a number of cemeteries have not yet been included and some cemeteries are only partially researched.
I hope this helps (if you haven't already tried the above sites).