Dan, I couldn't find his wife's name but I think he was the brother of Jacob Eckler Jr. The junior was to differentiate him from his "Uncle" Jacob Eckler Sr (Ulrich's brother).You can find a little more info in "The Kentucky Genealogist" July/Sept 1981.My line is thru Jacob Sr. There are three counties that you may want to check into Carroll, Baltimore or Frederick Counties, all three of Maryland.
The Ecklers migrated to KY from Maryland about 1795 along with the Lemmons and other related families. There was a lot of marrying between the Eklers and Lemmons, so you may want to take a look at them too. Wish I could help more... Let me know what you find out. Thanks Deborah