I don't specifically see the connection to 7w8 and ENP, to the contrary I would say EXTP and Te heavy EXFP. 7 has an EXXP-ISH feel about it (distract self, avoid pain, live in the moment, have many hobbies, don't waste life) and 8 I associate with Te and probably the stereotypes of STP, I have 8 in my tritype as a last defense thing, and was raised by a Te heavy family. It is more of a learned thing, which enneagram is a lot more about childhood and life experience and the way you responded to it instead of more of a sense of being hard wired to an MBTI type or Keirsey temperament.
I honestly don't associate any of those enneagram more with a stronger intuitive function. Like for example it seems many INTx would be 5s, but I think ISTJ can also very much lean towards 5 because of the success Si dom has in traditional school or business, combined with a thinking preference.
Have you done a lot of research on enneagram?
