Thank you for looking. I consulted the Illinois database earlier and came to the same conclusion. Upon further review I doubt that if Edward served in the Texas-Mexico conflict that he enlisted from Illinois.
According to the "History of Bureau County" (Illinois) published in 1885: "Edward Hall, like his brother Reason B., was regarded by the new settlers of the Indian wild waste as that strange being, an Indian fighting, daring pioneer, who took an active part in that prolonged tragedy that gave this great valley to civilization. He was a single man; he came here in 1829 and settled on section 34, in Hall Township. He built a cabin where Jacob Wasson afterward resided, but the next year left for the wilds of Texas."
So, he apparently left Illinois for Texas in approximately 1830.
I found a reference to "E. H. Hall" who served as a sergeant in the Company of Washington Cavalry on a 3 month enlistment June-October 1836. This E. H. Hall served under Captain W. H. Secrests. The record is from the transcribed roll "Muster Rolls of the Texas Revolution" maintained by the Daughters of the Republic of Texas.
Perhaps this E.H. Hall is a lead worth pursuing.
Does anyone have any information about the Washington Cavalry, and what actions they might have been involved in? My Texas history is a little rusty.