Online tickets for regular entry to the Vatican Museums are currently sold out all the way through May 2, so I think your chances of being able to buy same-day, regular tickets online in October are zero. Some Vatican-operated tours are available for dates before May 2, but you'd have to fiddle around with the booking calendar to see precisely when tickets are available for English-language tours (assuming that's what you'd want). A date will appear to be available even if there's just one time slot still open for a tour in any language.
https://tickets.museivaticani.va/home/calendar/visit/MV-Biglietti/1
I don't think walking up late in the day will work, either. The Vatican Museums do hold back some tickets for sale on site. That's why there are always two lines for entry. The one that moves rapidly is for people who've purchased online entry reservations in advance. The one that crawls is for people who still need to pay for entry. I assume at some point during the day, all of that day's held-back entry slots are gone.
Perhaps we have someone on the forum who has tried this recently enough to give you a first-person report.
