Elisha's parents are not known, but there was a Gibba Goodman on the Logan County Tax lists from 1804-1806 having 150 acres on the Muddy River. We cannot know everyone who was in a household by looking at these tax lists, but they do show one male over 21 and one male 16-21 years of age. It is of interest to note that Elisha had a grandson named Gibby.
There is an Elisha Goodman listed in the 1810 Census of Butler Co., KY. There are a woman and a man listed as being between ages 16-25 and two male children between 0-9. That would fit this family.