I decided to look into what the Illinois state constitution says about all this. Enshrined in said constitution is a clause which basically says that all able-bodied adults who are citizens of the State of Illinois are militia members. This is obviously to dovetail with the US Second Amendment.
So, being an able-bodied adult who is a citizen of the State of Illinois, I contacted my state representative and senators, asking what were my rights and responsibilites as a member of the Illinois state militia. One person actually called me back, but the voicemail he left was very dismissive, saying that he could look into it, if I wanted to waste his time.
This does not suggest that the "militia" in Illinois is "well regulated."