You were doing great right up until that last sentence.
If the pitcher fails to "take, or simulate taking" a signal from the pitcher's plate (ie: make a discernible pause with the hands separated), you have one of two possible outcomes.
If the pitcher pitches before the batter is set and ready, then it is a quick pitch. The ball is dead and "no pitch" is declared, not illegal pitch. There is no further penalty. Everybody resets and we go again.
If the batter is set and ready, but the pitcher fails to take the required pause, it is an illegal pitch. The ball remains live and may be batted into play.