From my experience these sorts of conversations come much more easily in rural diners and country grocery stores than NYC bars (or at least places where people aren't generally trying to "be" someone). And it really doesn't take much tuning of any personal social instrument, just a willingness to lay one's own instrument down and enjoy the unique sound of another's.
I'm trying and failing to imagine how one would strike up a deep conversation with a stranger at a grocery store or at a diner, except maybe one of those diners that has counter seating which resembles a bar. As for the rural part, I have no idea why it would matter.
