Isola Giglio in October

Haven't been to Giglio but loooove this area. I think I would take the car for a day trip in October. That way, you can get a good lay of the land without having to be selective, plus in October it could be very quiet without tons of services on offer. I'd plan on doing some exploring, then have lunch, then maybe do a hike with return ferry schedule permitting.
You can also rent bicycles: https://www.traghetti-giglio.it/en/tp-magazine/giglio-island-by-bike-itinerary-on-two-wheels/
You should of course make sure your rental contract approves of ferry travel, and don't drive on any roads that could leave you stuck (ask me how I know...).
https://www.tripsavvy.com/complete-guide-giglio-island-italy-4584777

The question is: is the car really necessary? I left the car at Porto Santo Stefano (there is a lot across from the ferry dock) and visited on foot and by bus. The 3 towns are connected by bus. They also have taxis, or you can rent also e-bikes, if you don't like scooters. It's up to you but ferrying the car across costs about 100 euro round trip (I was there in July 2018, so it might be a bit cheaper in Oct), so not sure if it's worth it for a day.

Thank you both! Yeah I was worried about a lot being closed and less bus/taxi availability after season.
I will ask- how do you know about cars getting stuck??

The buses work year around. People do love there and they need transportation. The island is not that car friendly. Roads are narrow and parking limited. The main roads that connect the 3 villages are paved, but in any case you should not take a rental car on dirt roads (not allowed by contract). If you take the car you need ferry reservations. For passengers only no need to reserve anything. You can walk in to the ferry and go.

Ha, luckily I have had no disasters, but I have been led deeper into an olive grove than I would have liked (never trust GPS). I just figured it was prudent advice after glancing at the map and seeing what the roads are like.
I think it overall depends on what you want to do, as for sure you can go from town to town by bus. If you are up for the biking, then that would probably give you sufficient access to some hiking trails if you were interested in that.
You might also post on Trip Advisor to see if you can catch someone who has been on the island in October. It can be hard to have a sense of what a place is like outside of season.

Thank you all for the advice- we left the car and used the bus. It was simple and inexpensive to see both sides of the island. Very quiet in October- too cloudy to see from Castello so stuck to shore areas.