Can a single woman who is eight years older than me pursue it?
First of all, you should find out why she refused you. If she secretly loves you, but refuses you because of her age or other people's eyes, then you can persist in pursuing her, tell her clearly that you don't care about your age or other people's ideas, and bring her to your family and friends to let her feel your sincerity. If she doesn't like you, then you have to weigh whether to give up.