Are there any success stories of people becoming a mentor to someone because of a cold email? That sounds like a lot to ask for considering how much time it takes to mentor.
I drove to the nearest university, walked into the physics department office, and asked to speak to the chair. The chair was busy, but the vice-chair was more than happy to chat for 20 minutes.
The vice-chair then took me to a researcher's office, and we chatted for half an hour. That researcher then introduced me to a group professor, who offered my an unpaid-technician job a few days a week.
After a couple months happily toiling in the lab, often alongside the PI, I was asked to change to a full-time paid position.
A year into that the PI asked me to join the graduate college. I earned a PhD from the group 6 years later.
It all worked very nicely for me, and every person was lovely and encouraging through the whole process - regardless of my audacity in asking for the chair!
If you're coming in from outside academia, be prepared to have useful skills/knowledge to bring to the collaboration and a clear ability to commit enough time to be valuable. Expect a much lower conversion-rate. Most people that academics encounter with cold emails (at least in physics) from the outside are insufficiently prepared or advancing a pet (usually demonstrably-incorrect) theory.
If you email the right person with,
"Hi, ISL!
I'm j7ake, and have a ton of experience with X (link to resume) and am really interested in learning more about experimental gravitational physics. I've read several of your papers [1,2,3], and your work is really interesting.
It looks like you might be able to use X to improve your results with Y -- might you have a little time to answer some questions about your group's work and see if there's a way I might be able to help you put X to good use?
Thank you!
j7ake"
you'll get replies.
I've also emailed another academic over a month ago about an article he wrote abiut a type of non-profit I'd love to set up, and haven't heard back. Though when I emailed him last year it did take 6 weeks to respond. I just wrote this to say I feel it's very hit or miss, depending on the academic in question.
If you can bring value to the relationship (sometimes interest is enough, but not always), that will make a big difference.
An HN-specific skill that might provide a mutually-beneficial "in": An ambitious experimental collaboration run by some of my physics colleagues once engaged some CS students to overhaul the collaboration's web-page. The result was one of the nicest research webpages in the (large) department.
Offering something like, "I'd really love to learn a lot more about your research -- I've built out a number of sites [1,2,3]. Could I work with you to improve your research group's page in return for helping me understand the subject-matter better as I go?" may get some replies. Make sure the relationship is mutually-beneficial and not exploitative :) (at a minimum, it can go on your resume).
I imagine there are jerks out there but honestly for a lot of people this is something they have poured a lot of themselves into (especially in academia) and its nice when someone is new but actually really interested.
I think a lot of PIs in less popular fields struggle to find computationally proficient candidates. There is a massive glut of software talent in certain hot-button domains and a huge shortage in others