Cana you explain extended eye contact in a conversation?

I’m used to people looking at me, looking away, looking back, etc, etc, as we talk. I’m used to having extended eye contact only with people who are really intensely interested in me. This morning, I was waiting in a line outside the taco truck in the rain, and some woman asks to share my umbrella. We start talking, and she holds her eyes steadily on mine. I don’t know how to describe how it makes me feel. Her eyes look beautiful, and I have this feeling of sinking into them, and of course my mind is telling me that I don’t know this person, and this makes no sense.

This is the third time this has happened in the last couple of months. I don’t recall it happening before. The other two times were with clients. I found myself feeling this sense of connection with them that didn’t make sense, and seemed a little dangerous.

Does this happen to you? What is it like for you? What do you think this means?