positano - after "tourist season"

I really cannot be of help, but did want to share this website which you may or may not know about.
Were you planning your trip 12 months in advance looking at this site a few times could likely answer your question as there are 8 different cams covering the Amalfi Coast area including 2 in Positano.
https://www.skylinewebcams.com/webcam/italia.html

I was there in October and was under the understanding from personal observation and from talking with folks in the service industry that the really busy season had just ended but it was still quite crowded in October, you wouldn't call it a slow time if you did not know otherwise. All bus services and boat services where running, though the boats in days of high seas or rain did not run, that may be true all year though.
I am sure at some point it really slows down but not sure exactly when that is.

Thanks!
The webcams are great.

Ferries run year-round, weather permitting, from Sorrento to Capri and Naples. Rick's book implies that TravelMar might run Positano-Amalfi boats in the off-season, but not any longer distance boats to or from Positano. Most of his hotel and restaurant listings include closed periods. I think you'd find more dining options open in Sorrento, where more people live year-round.