Meaning of "spotted something, and I’d be home"?

Hello everyone. I am reading a novel, and I came across this expression. Could you please let me know its meaning?

Just when I was about to leave Straus Park, I took out a five-dollar bill and snuck it into the hand of the beggar woman. Por mi padre.

[Officer Rahoon speaking] “Seriously?”

[The protagonist speaking] “Let it rest, Officer,” I said. You never know, I wanted to say. In another age, the old hag would have asked me to sit on one of these benches, brought a bucket to wash my feet, spotted something, and I’d be home. Y por Clara también. I should have added.

- André Aciman, Eight White Nights, First Night

This is a novel published in the United States of America in 2010. This novel is narrated by the nameless male protagonist who meets Clara at a Christmas party in Manhattan. At night, the protagonist leaves the party and heads towards a nearby park called "Straus Park". There, he sits on a bench for a while, and a police officer named Rahoon approaches him to ask whether everything is okay. So he talks with this officer as to how it has been a year since his father died. Then a beggar woman approaches them, and the protagonist gives her some money.

Here, I wonder what the underlined expression means.

My guess is that the beggar woman "noticed something (=spotted something)" and "I would feel as if I was at home (=I'd be home)", but I am not sure about my reading.

What would it mean that she "spotted something" and "I'd be home"...?

Thank you very much for your help.