Arleigh..... Have you thought to check to see if William Henry Musick belonged to a GAR post in Eudora after the Civil War. Also you might want to check the Kansas State Historical Society's newspaper collections to see if Eudora published a newspaper after the Civil War which might have referred to your ancestor. Then there is looking up references to the 106th Illinois Infantry for reunions or regimental references.

The same goes for your Confederate ancestor.

Hope this helps.