Steam train ride would be awesome! Plus this one takes you to a fall harvest festival, very neat.
I see the full schedule for the steam trains on this page: https://www.ferrovieturistiche.it/it/fvo/
Is this also where you found it? If not, it could explain why you didn't see the booking info at the bottom of the page:
SOLO SU PRENOTAZIONE - Per informazioni e prenotazioni del Treno Natura:Agenzia Visione del Mondo
Telefono: ++39 0577 48003 - 281834
I see that the ones in blue have links to pdfs that include program for the day but it isn't yet available for October. I doubt they have a definite program, other than likely following past programs.
I would suggest you contact the agency listed above for a full program and more details on where you depart in Siena. It seems all of the other itineraries depart from the main train station in Siena, although it isn't specified, it is the only train station in Siena
Most of the other days that have the pdfs show that they left Siena between 8.50-9.00am. Most are back in Siena before 6pm, with one or two arriving back by 6.30pm. The cost for all of them is 41€ which includes insurance and booking fees.
I just used the web's archives to find the 2019 program, which is likely very similar to what will be planned for this year: https://media-ferrovieturistiche-2.s3.amazonaws.com/allegati/VAP._AUTUNNO_19.pdf
From this, you can see you do partially with steam train, with the last part by bus (Abbadia San Salvatore is on Monte Amiata). Depart around 9am, return around 6.30pm. It also says if you book the restaurant they offer, you can go collect chestnuts with their group so if they do that this year, I would recommend you do that part.
Looks good? Please let me know how things turn out