I've no personal experience here but this traveler's experience in Florence may be useful:
https://autismadventuresabroad.com/accessible-italy-why-florence-should-be-on-every-autistic-travelers-bucketlist/
Their counsel was to have a doctor's note certifying the disability, and I'd carry a card with the statement "Mio figlio/figlia è autistico" (My son/daughter is autistic.) I think this is especially important if that disability isn't visible, as can be in the case of autism. My hunch is that your bigger issue is trying to avoid advance, timed-entry tickets for the Colosseum. The colosseum's website states this:
"Individual visitors who are entitled to free tickets according to the law must book the entrance on ticketing.colosseo.it/en"
As well, the parent who isn't covered under the caregiver clause (he is only allowed one) would need a full-priced ticket, and you may need to book the free one for the caregiver.
Could you try and stand in line for them? I wouldn't: that line may be very, very long, all of you MUST be together to purchase them, and I'm unsure they'd provide the free tickets at one of the booths, although they might. That wait in line may be difficult for your son/daughter and he/she might be 'done' before ever getting inside.
Vatican Museums state that the visitor's disability must be 78% and free tickets cannot be issued in advance, though the visitor is allowed to skip the queue.
https://www.museivaticani.va/content/museivaticani/en/organizza-visita/servizi-per-i-visitatori/accessibilita.html#:~:text=Secondary%20navigation&text=The%20Vatican%20Museums%20offer%20free,also%20extended%20to%20a%20companion.
You're going to want to be cognizant of the very heavy, very loud crowds at some of the attractions if that sort of thing bothers him. You didn't mention visiting the Vatican but the crowd and noise levels at both the basilica and museums can be pretty intense. That shouldn't be as big an issue at Pompeii, although we found some the crowds inside the baths and a few other interiors to be a bit much. As it sounds as if he/she is more into ancient history, there are alternatives to the Vatican that would work for him/her, such as the Baths of Caracalla.
Hopefully you'll hear from someone who has traveled in a similar situation. In the meantime, you could write the offices at the Colosseum and Vatican for what they'd recommend so you know more exactly what to expect in advance? Down in the very bottom right of this page of the Colosseum's website is an icon of Nero (fellow with a crown) that's the link to their live-chat function.
https://colosseo.it/en/2023/04/free-tickets/
Vatican's contact info:
+39 06 69883145
[email protected]
