died on June 8th 1889 in Snyder County Pennsylvania
One way to do this is to find an overlap between his known Location/Date of Death and a primary source proof of veteranhood.
1) Find someone with a newspapers.com account to do a search from 08JUNE89 to about the end of June 89, for an obituary in Pennsylvania papers (you might find him mentioned in a publication some distance from the county and veteran status was often part of the writeup).
2) The PA records are here, but might be a forelorn hope
The records provide little genealogical information.
Mexican War Records
www.phmc.pa.gov
3) Post a request on FindAGrave for someone to take a photo of his headstone (if he has one). Might be a government issued one.
Calculated date of birth from age at death.
www.findagrave.com
4) See also
https://www.ancestry.com/search/collections/8750/
5) An 'Abraham Kauffman' shows up as a hit on Synder County's listing of war veterans, but under CIVIL WAR.
This gives you more data points to work with, since a 40-ish veteran would be an ideal candidate for an NCO/Officer slot during the mad scramble of 1861. If A.B. Kauffman turns out to be Abraham Kauffman Synder Co civil war guy, then
his pension package might mention Mexican War service (and you'd get a two-fer from your efforts).
Note - not to be confused with this Abraham B Kauffman of PA
The son of John & Elizabeth (Brenner) Kauffman, Abraham married Elizabeth Smith on February 13, 1853, and fathered the children you see linked below. In 1860, he was a cooper living in Millersville, Lancaster County, Pennsylvania, and stood 5' 4 tall with brown hair and blue eyes. A Civil War...
www.findagrave.com
6) Look for Abraham Kauffman Civil War guy's service to be in a regiment with a term of enlistment / discharge date in mid-to-early fall 1864, as baby Abraham came out of the oven in June 1865.
https://www.findagrave.com/memorial/173824717/abraham-g-kauffman
Note: he doesn't appear on this Snyder County list from Bates (usually pretty accurate) so he might have enlisted in a Regiment from outside the county
http://genealogytrails.com/penn/snyder/military/3yr_records.html
7) IF there's a widow's pension packet on FOLD3, expect your MexWar/ACW candidate's second wife Annie's name to be all over it.
Pennsylvania, Death Certificates, 1906-1964 Name: Annie M Kauffman [Annie M Schoffer] Gender: Female Race: White Age: 85 Birth Date: 29 Jan 1872 Birth Place: Port Trevorton, Pennsylvania Death Date: 30 Apr 1957 Death Place: Decatur, Mifflin, Pennsylvania, USA Father: Jacob Schoffer Mother...
www.findagrave.com