I think I am a direct descendant of the Tom McEldowney you refer to. His wife Erma Gibbons is my great grandmother. Their daughter, Thelma Faye McEldowney Bradley was my grandmother. I found the same pension request card you refer to via ancestry.com
I would be very interested in anything you know about Tom McEldowney's lineage and where his grave is located. I have no information on his parents, place of birth, or anything else until the 1910 census.