Beta NFs are considered to be "dark" or at least darker than Alpha SF in terms of emotions. I feel like there's a connection because many fictional IEIs have been in these types of stories; Romantic tragedies such as Ophelia from Hamlet, Juliet Capulet, and Desdemona from Othello. IEI as a type tends to also be identified with people who are INFPs and enneagram 4s, and I'm sure you know the stereotypes among that type combo.