I think you could definitely do the same thing to learn relative pitch. In western music theory there's generally only 12 notes. And #1 and #12 are the same, an octave, which many people can recognize implicitly

Furthermore, while a piano might have 88 keys (still doable with practice) most actual music rarely jumps more than an octave or two.

Generally, music is also further restricted to a key/mode of 8 notes, again with 1 and 8 being the octave, which you probably already know

If I were to teach myself again, I would first find a reference for the intervals 1-8 in a major key and in a minor key. Or learn the full 12 at once if that's more sensible to you. For example the main theme from "Jaws" is a minor 2nd (2/12. Or the song for Happy Birthday (in the USA) starts with a major 2nd (3/12). I had a few more examples, but this Wikipedia article seems to have far better information than I could give you https://en.wikipedia.org/wiki/Interval_recognition

You could also just try to listen to music, possibly at half or quarter speed (easy to do on YouTube), and try to write down the notes, and checking your answers, I'm sure that could work.

Best of luck!!