Here's my experience last February. I would expect a lot of traffic in September - even late September.
It's nothing like New York. It's mostly a narrow 2-lane road along the cliffs, often no shoulders, rock face on one side and a low stone wall on the other side, blind curves and lots of up and down. GPS isn't needed - the road is obvious. And if you venture of the main road into one of the towns, you'll always find your way back - if you went up, you have to go down, if you went down, you have to go up. These are small villages nestled on the cliffs. There's little public parking. I didn't stop in Positano because I couldn't find a parking place. In Amalfi, I had to wait for a place in the main lot. . . . in February. OTOH I did find places to pull over for a few minutes for a photo op. I doubt that would be possible in September.