At a recent networking workshop (not one of the "just don't be an introvert" ones, an actually helpful one with applicable ideas) I learned that it is supposedly very common to have a (career) mentor in academia. This is not meaning a supervisor or a former supervisor you are still in contact with, but a person a few years further in their career than you, not necessarily exactly working in the same field but well established and experienced in some aspects of academia and academic careers where the mentee is in need of guidance (networking, public outreach, being from a similar minority, whatever is important to the mentee).
I promptly started to figure out what I would need in a mentor, who could be a good mentor and now how to approach them. But the questions come back nagging, because while this all makes sense and an online research came up with many tips and mentoring schemes I still have never met someone who said they had a mentor in this way.
So the question is: Do people have mentors in academia? If so, what are your experiences as a mentor/mentee? And would it be appropriate to ask someone who you have never met before for an informal conversation because you feel they might just be right for you?