I think Holmes would be assessing the potential spy in more detail. What about this for an inner monalogue.
I did not stare back as I wanted him to think I had not noticed him. Instead I looked out across the street several times, but never for long and always pretending something or someone else had caught my attention. How I hoped that he would move and give something about himself away. If he moved with the ease of a younger man that would indicate a disguise. Perhaps some other clue would emerge. To my frustration he did nothing that might give anything away.