The formal request, will you be my mentor, puts an undefined and open-ended obligation on a person who barely knows you. It is why the answer is so often a polite deferral. Real mentoring relationships almost always start smaller and become mentoring without anyone naming it.
Start with a question, not a relationship
Approach someone with one specific, answerable question about something they genuinely know. It costs them five minutes and it gives them the pleasure of being useful, which is the actual currency here.
If the exchange goes well, ask another one a few weeks later. Three or four of these and you have a relationship, which you can then deepen.
Look for people one or two steps ahead
The instinct is to seek out the most senior person available. Someone twenty years ahead often remembers their early career inaccurately and faces completely different problems.
Someone two or three years ahead of you remembers exactly what you are dealing with, has current information, and has far more time. They are usually the more useful mentor.
Use your existing surface area
Most mentors come from places you already touch: a former manager, a colleague on an adjacent team, someone you worked with at a previous employer, someone from a course or professional group.
Cold outreach works too, particularly to people who write publicly, but warm connections convert far more often.
Make it easy to say yes
Be specific about what you are asking for and how long it will take. A request for a twenty-minute call about a defined topic is answerable. An open-ended request for guidance is not.
Offer to work around their schedule entirely, and mean it.
Come prepared and follow through
Arrive with two or three specific questions and enough context that they can answer without interrogating you. Take notes.
Most importantly, act on what they say and tell them you did. Nothing sustains a mentoring relationship like evidence that the advice was used. Nothing kills one faster than repeatedly asking for input and ignoring it.
Do not expect one person to cover everything
The idea of a single mentor who guides your whole career is mostly a story. In practice people have several partial mentors: one for technical depth, one who understands the politics, one who knows the industry.
This is easier to build and more useful than searching for a single person who does not exist.
Give something back
You have more to offer than you think, especially to someone more senior: a perspective on how a change landed with your team, awareness of a tool they have not used, help with something small.
A relationship where value flows only one way quietly runs out. One where it flows both ways lasts for years.
Accept that some will not work
Some conversations go nowhere, some people are too busy, some advice will not fit you. This is normal and not a verdict on you. Approach several people, keep the ones where the exchange is genuinely useful, and let the others lapse without ceremony.