But here's a tip. Whatever your calculus. For whatever the end. Recruiting mentors is a vastly underestimated skill.
Yes, very much so (retaining them is even more difficult!) As I have written elsewhere getting several mentors is very important at every stage of your career. I think I was probably not a very good mentee but have learned from my ways. And having mentored several students, I know very quickly who to dump and who to keep. I don't think students really understand the art of being a good mentee, so I am going to explain this:
1. remember to always work around your mentor's schedule, they are taking the time to help
you. no matter how busy you think you are they are even busier
2. always reply as quickly as possible to any email, even if just to acknowledge. never wait several days to do so, there is never an excuse to do so.
3. if you are working on something with your mentor, give them updates of how you are doing, don't wait until you have something to show them
4. it is up to you to put in the hard work. you will only get as much out of the mentoring relationship as you put in. if you want opportunities, ask for them, make yourself open, be the first to suggest something, be eager and responsive
5. remember that many people in academic are fragile narcissists and part of your job is to inflate their egos. conversely, be mindful that the smallest perceived offense can shatter your relationship and potentially your reputation (this was always my biggest failing and surprise as a mentee)
6. remember it is on
you to schedule time to meet with them, not wait for them to suggest it. If you want regular meetings,
you should be the one asking for it. It is always okay to ask (not demand). those who don't ask, don't get
7. keep them informed of how you are doing (for example if you have won an award, published a paper etc etc), don't be shy about doing so
8. don't feel like a nuisance, it is okay to keep pestering (within reason - get the hint if you've ruined it)
9. formulate goals for what you want from the relationship and from your future
10. be appreciative and respectful of the time, effort and interest your mentor is putting into you