Hi
If you are willing to invest in it - try career leader (
https://www.careerleader.com/). Aside from providing career advice based on your advice, it also allows you to get 360 degree feedback from different people. I found it useful to ask my recommenders to provide feedback on it confidentially, where I only see the aggregated average ratings, and not the individual ratings of people - it gave me a clearer picture of where I need to improve, and gave them a clearer picture of what they thought were my weaknesses. I have seen that for most people, as long as feedback is perceived as confidential, people will have some idea of what a person's weaknesses are and will articulate it.
Of course, I realize not everyone may want to buy it, especially since as a student, you may get free access to it.
The next option is to have a frank conversation with your mentee and ask him to be candid in what he thinks your weaknesses are. If your mentee feels comfortable sharing this information with you, he is sure to think of something, however minor.
The other option is you list a three to four weaknesses you perceive in yourself and ask your mentee to pick one that he concurs with. And yes, you may want to pick weaknesses that you may have started working on improving already, or can be improved easily.
Hope this helps.
H