I don't have any information on Patrick's parents - (Patric and Catherine Finnegan) but I have written up a bit on Patrick, as my interest is McGough's in Upstate New York. I would suggest the possibility of a genealogist or centre in Louth that might have a lookup in a graveyard, however, you may be already pursuing that path.
In the meantime, I'll send you what I have on the family.
Patrick McGough was born in County Louth in 1829. Patrick emigrated to America in about 1850 and on November 20, 1857, he petitioned to become a citizen in the City of Milo.
A blacksmith by trade, Patrick lived, owned and operated a blacksmith shop in Milo Center. The location of the family's home and blacksmith shop can be seen in the following map.
[can send if you would like]
You'll notice that the McGough's home and shop is located in the center of town on the main road, easily accessible to all those passing by and nearby residents. The blacksmith shop was one of the first priorities in any new settlement. A blacksmith was an integral part of any settlement. He crafted and fixed the farming instruments such as plows, created nails, horseshoes as well as shod the horses, performed wagon repairs among many other critical duties that kept the community working and productive.
As a blacksmith, Patrick would have worked daily at a forge --a brick or stone hearth about waist high with square fire-hole on top. A grate held charcoal and allowed ashes to fall into the ash pit below. A hold just below the level of the grate allowed a nozzle, the tue iron or tuyere, attached to a bellows, was inserted for fanning the flames into an intense heat. The Anvil, about four feet in front of the forge, was a heavy mass of forged iron resting on the butt of a log set in the dirt floor. The different shapes on the anvil allowed for different degrees of bend and the Chisel, allowed the smith to cut the red-hot metal with a blow of a mallet. Patrick undoubtedly was a toolmaker - once he had his forge and his anvil, he made the rest of his tools; then he could proceed to hoes, cowbells, cobbler's awls, tanner's scrapers, plane blades, ax heads, etc.
Patrick McGough married Julia Sanders (orginally of County Cork, Ireland) and had seven (7) children: Patrick (b.1850 - d.1884), Thomas  (b.1852 - d.abt.1863), Mary (b.1853 - d.1902), Rose (b.1857 - d.1908), Charles (b.1860 - d.1943), Thomas  (b.1863 - d.1907) and Katherine (b.1865 - d.?).
The couple does appear to have had two sons named Thomas. Thomas  born in 1852 last appears in the 1860 census as 8 years old, attending school. By 1865, Thomas  is missing from the census, but instead there is another Thomas  who is listed as the youngest child of the family at age 1 1/2.
In 1863, Patrick appears on a Civil War enrollment list subject to perform military duty. I have not located him as a soldier in any NYS regiment. Perhaps as a father of six and one of the town's blacksmiths, he was too valuable to be sent to war?
Patrick's two sons, Patrick Jr. and Thomas  followed in their father's footsteps in the blacksmithing trade. Tragically, Patrick Jr. was struck by the cars in the train yard in Himrods in 1884. Thomas continued on the family tradition, until the late 1920's.
Patrick McGough was an integral part of the community until his own death on February 27, 1881. He is buried at St. Michael's Cemetery, Penn Yan, NY.
Listing of Persons & Dates
b. 1827 in County Louth
m. to Julia Sanders (b.1832 - d.1889)
Patrick McGough (b.1850 - d.May 23, 1884)
Thomas McGough  (b.1852 - d.abt.1863)
Mary McGough (b.December 1853 - d.August 22, 1902)
m. to John McGough in Town of Milo, NY
Charles McGough (b.1877 - d.October 17, 1961)
John H. McGough (b.1878 - d.October 30, 1959)
m. to Mary H. Murphy
1 child: Mary E. McGough b.1906 - d.1996)
Anna Rose McGough (b.1894 - d. November 1, 1980)
Albert George McGough (b.1896 - d.July 1981)
m. to Alice Maloney (b.1894 - d.1956)
Charles McGough (b.1860 - d.1943)
m. to Margaret Costello (b.1862 - d.1937)
2 children: Thomas F. McGough (b.1884 - d.1940)
Louise A. McGough (b.1887 - d.?)
Rose McGough (b.1857 -d. May 28, 1908 in Texas)
Thomas McGough  (b.1863 - d.March 1, 1907)
Katherine McGough (b.1865 - d.?)
d. February 27, 1881 - Town of Milo, NY
buried: St. Michael's Cemetery, Penn Yan, NY