Rule of Thirds doesn't really work for a lot of photography. When you're shooting images in the street it is infinitely more important to keep all the moving pieces in mind, consider how they interact with one another, and then to capture the image when they all line up.
I really consider the rule of thirds one of the most over-valued guidelines in any art or craft. Good image composition hasn't changed that much. Look at paintings by old masters, and see how those work. You learn more there than here.
Look at this Vermeer: Are there thirds? You bet! there's the giant negative space at the top and right, and the table is about a third of the way down... but the subject is centered. It would be a totally different image if you cropped the right, placed her on a third axis... you would lose the contextual details... the tiles at the bottom, the little coffee box on the floor...
Look how Edward Hopper deliberately painted an image with half a table and lamp... I think I would have tried to get them all in the shot, or exclude them... but there's no 3rds at work here... although you could argue that she is placed along the lower horizontal third axis...
Look, there's plenty of opposite examples of where the rule could be found. It's not clear that it is deliberate. The point is that an image can work, regardless of the rules. We live in such a visual world right now that you know pretty well what works, and what doesn't. I don't think there are rules to guide you though.