Frank,
I was not able to find out anything about T J McDonald in the Illinois Muster Rolls. I found Terrence to Thompson McDonald but no one fits the criteria of TJ. All of the T. McDonald's except Thompson were discharged from the service. Thompson died at Bridgeport Alabama on Dec. 1, 1863. The state records do not show anything else. Perhaps he was from Illinois but served either in the regular army or from another state. I would think that Jim Martin might be able to help you out with this or perhaps Alan Pitts. I am sure that one of them will see your post and respond or you can contact them by clicking on the add at the top of the page. Frank