Still looking for the parents of Gertrude, daughter of Emma, born about 1889 in Illinois, huh?
You might need to ask your older living relatives to see if they know something. And, even then, there's no guarantee you'll find out much. Illegitimate children were very shameful back in those days. My grandfather was illegitimate and my great grandmother put a fake father on his birth certificate just to make it look good. To this day, we only have speculation and have no clue who his real father is.