Today I was staring at a girl in public without even being aware of it, I was just spacing out, and she made eye contact with me. I maintained eye contact for a few seconds then looked away, since I realized she must have thought I was staring at her and "caught" me. Her expression was completely neutral throughout. Later her mother also showed up (the girl was not underage though).

What should I have done instead? Maintained eye contact until she broke, and smiled at some point before that? I didn't want to seem sexually aggressive as this was in a waiting room and I wasn't at my best.