I'm still working on his background, but it appears that Andrew (or Andreas) Finck was an ancestor of Jacob I. Eacker (the son of the above mentioned Judge Jacob Eacker and the husband of Gertrude Herkimer, the daughter of Captain George Herkimer and niece of Gen. Nicholas Herkimer).
I'm finding that many of these families immigrated from Germany together and settled in NY together so it is not surprising to see them intermarrying and to see many of them fighting during the Revolution.
So far, it looks like Andrew Finck didn't let being in his mid-50s stop him from joining the Revolution. He served as a private and ensign in the 2nd Regiment for Tryon County, NY. His family was certainly patriotic: both his sons fought in the Revolution, including his son, Andrew, who rose to the rank of Major (it's been confusing however, because both the Major and his father were named Andrew Finck and it's been hard to determine who is who). The elder Andrew Finck's three daughters all married Patriots, including Margaret Finck who married Jacob Eacker (he's the great-grandfather of William H.H. Wilcox) who later became a Judge and served on the NY State Assembly three different times.
To read more about the younger Andrew Finck (Major Andrew Finck), visit here: http://www.fortklock.com/afinck.htm
I'm hoping to be able to share more about his father soon.