It’s not like I can tell you that much about this “other” self, as I’m still at the beginning of my self-awareness journey. ;) But I experienced this other concept of self to be true for me. These were the moments when I had an experience indicating that my consciousness is something more stable and lasting than the passing events in my mind (thoughts, feelings, etc.). This is what I meant by saying that my thoughts are not my identity.
Sure, I still often get an illusion that I am my thoughts, when I forget to look at them as passing events. This is when I get entangled in thoughts and take their content as reality. These are the moments when I still identify with my thoughts.
I’m not sure whether this answers your questions, but I don’t know what else to say. If you want to know something more specific, feel free to ask. I’ll do my best to answer.