You establish residence by living at a location with the intent to remain there indefinitely. The domicile concept comes into play most frequently when a state sues for back taxes. What you say you intend to do and what you really intend to do might be different. Direct any question to your old state's tax office and to the one where you wish to establish residence. They must be able to prove to a judge that they intend to move back to the state they are claiming to be a resident of.
Active duty can show that they are only in Illinois because of orders.
Retired people cannot show that anything is preventing them from moving back to their state of domicile. The appearance of hyperlinks does not constitute endorsement by the U.S. Air Force of this Web site or the information, products, or services contained therein. For other than authorized activities such as military exchanges and morale, welfare and recreation sites, the U.S. Air Force does not exercise any editorial control over the information you may find at these locations. Such links are provided consistent with the stated purpose of this DoD Web site.