That’s a very good question. Sorry for the long (and rather vague) response.
The first thing I do when something I can’t explain happens is retreat to the security of my firmly held beliefs. I think that’s pretty normal. I try to come out again and get some kind of external assessment of what my brain is telling me. Two examples:
A good few years ago, I started doing ‘psychic’ readings using the principles of cold reading, given I have (to my knowledge) no psychic abilities. I wanted to know why so many people were convinced their experiences of readings were real, and I know that dismissing those people as stupid or gullible was just not a valid answer. They weren’t. I never performed without people knowing I was not psychic, just showing them what a reading feels like using scientific principles. It still always worked incredibly well. I have now done hundreds of them.
There were some readings when things jumped into my head which were so accurate that they freaked out the sitter, and really frightened me. A number of times I packed up my gear and decided never to do it again. Always this was in public, with witnesses. Those who were watching the readings could often pick what I had run with, when I couldn’t remember certain aspects of the earlier interaction. I talk a lot and move fast when I am reading, trusting intuition and the experience of doing this a lot of times. But there are still a few instances which really seem to me beyond coincidence, cold reading, or experience. But I can’t replicate them, so how can I know what really happened and what is my brain reconstructing it to fit? So I explain it to myself as still not being psychic, but that I just don’t understand. I don’t have the evidence to do otherwise.
Just recently something happened which I am working on for my doctorate. I can’t be specific because I don’t know where it is leading just at this moment. I visited somewhere and just seemed to have an understanding about the background to the place, with the most limited of knowledge and insight. I just knew. I have now been working on this concept for seven months, with all the resources of a university, academic librarians and my supervisor, and have found so much to back my ideas that it is ludicrous - so much that I knew nothing about. Looking back, with the lack of knowledge I had, I now can’t see how I knew what I knew with such confidence. But now I don’t know for sure if I am twisting the evidence to fit my beloved theory and thereby deluding myself that everything seems to fit so perfectly.
The only way I know to test it is to put it in a formal format and then put it out for others to assess, which is exactly what I am doing. It has to be someone other than my own brain which assesses what my brain believes so firmly.
I guess I just always try to find way to externally assess what my brain is telling me. I have no idea if that makes any sense to you, but that is how I have reacted to such experiences. They have never come in dreams, though.