If you want a more detailed scenario: you, more or less exactly as you are right now, exist in the / a strangers universe. You just had an encounter with a stranger, and the circumstances around the encounter are such that it is impossible for you to deny it really happened. What now?
I live in a major city, so if I was a sensitive, I probably would have had brushes with them before now (age 22) in ways that I could write off as dreams I mistook for memories, or shapes I misinterpreted out of the corner of my eye. I'm not a conspiracy theorist, but I like reading about them and things like "real" aliens, esotericism, the occult, etc. because it's an interesting, "magical" view of the world, and it makes sense to me that strangers would leak into that in-universe as cryptids and demons and other supernatural entities. So I would know there's people who believe these things are real, and I'd want to believe it, too... given some evidence.
A one-on-one encounter would probably push me over that edge. I can easily see myself becoming obsessed, dedicating all of my free time to finding other sensitives online and any information that's been accumulated about strangers, and probably spilling over into real-world conspiracy theories too because, man, if all those people I thought were crazy were right about one thing, maybe they're right about the Illuminati and stuff, too. I'm big on the gathering, organization, and maintenance of information, so I would investigate strangers personally and document things extensively, working with whatever community I could find to better our understanding of what's going on. This newfound "for the good of everyone" sense of purpose gives me drive until I die, either from something mundane or a fatal encounter with a stranger. In the meantime I hopefully manage to keep it together.
I'm pretty confident that's how that version of me's life would go. What about you guys?