Gilbert's ancestors are unknown. I suspect that Gilbert didn't share his family history with his own children. Much of what we know about his life comes from the Beer's biography of his son, Christopher Colombus Cool, who reported that his father was born about 1794, vice 1798, as indicated by census data. Christopher Colombus Cool also reported somewhat vaguely that his father was from "east of the mountains." He doesn't mention his grandparent's names, although many similar biographies include the names and some information on grandparents and even great-grandparents. In the 1880 census, two of Gilbert's sons, John and Augustine, variously reported his birthplace as Pennsylvania and Maryland.
The family oral tradition holds that we were Scotch-Irish, and McCool before we were Cool. This is certainly possible. There were many early Cools and McCools in Pennsylvania. But if Gilbert's own children were unsure of his origins, the oral tradition cannot be accepted on face value. It's possible that this line derives from the Dutch Cools (Coles) or German Cools (Kuhls). It's also possible that Gilbert may come from Cooleys or McCulloughs, who also populated the region in the time of his parents. Or the true story may be even more surprising.
One possibility is especially intriguing. In his first appearance in the official record, the 1830 federal census, Gilbert is noted fairly clearly as "Coal" vice "Cool." And it turns out that in the 1798 tax assessment of Washington county, a Thomas Coal was noted, along with Augustine Moore and John McConnell, two individuals who took part in this line's earliest known history. So perhaps this Thomas Coal is the best candidate for Gilbert's father.