AAQ
To address this from a different angle,
“ Maybe it will help us (and you yourself) understand your position better if you could describe how it came to your mind to spend time speculating about who M might b. Did you read it in sichos?”
Yes
“a yeshiva teacher?”
Yes, we learned all about many things about moshiach and geula in an inyonei geula umoshiach shiur. For 4 years, in addition to time spent learning outside of school.
your parents?
A bit but no explanation
a Gemora?
Yeah of course. The 4 yeshivos who promoted their RY as a likely candidate.
something in Tanach?
The whole Nach is full of moshiach and geula, and of course in Torah there’s the Mitzvah of ir miklat which was never yet fulfilled, so that’s proof for geula, as well as the nivuah of bilaam. But I haven’t seen in tanach anything about identifying moshiach. Sources for that would be mainly that Gemara above, and the Rambam. And of course if you’re expecting the Geula at any moment (whoever isn’t is deemed a kofer actually) then it’s only natural to look out for anything related including his identity.