I passed Part 2 of the Illinois Accident and Health licensing examination only, how long do I have to wait to retake the examination?

You must wait 3 days to retake the examination.  Since you failed Part 1 (general), you will only need to take Part 1 again. You have 90 days from the original examination date to pass the part that you failed.  Past 90 days, you must take both Part 1 & Part 2.