buy seat resv in advance or as needed

I've never traveled by train in Italy. I'll be using a Eurail Global Pass this coming June/July, and I might want to take one trip through Italy from Nice, France, via Milan, to Zurich. I can see I'd need seat resv for two legs of that trip, but since it'd be after the summer timetable changeover, I can't find specific trains yet. I can only find trains for before June 9. So I can't check, now, if seat resv are still available on trains I might use. So my question now is: how likely is it that I could just show up on the day I want to travel, or maybe a day ahead of time, and buy the seat reservations I'd need to use along with my Eurail Global Pass? It it matters, I'd likely be doing this Sunday, June 16. I'm aware France severely limits seat reservations for Eurail Pass users. I have no experience at all with Italian trains. Does anyone who has such experience think I'd be shut out, or could I take this chance? In any case, it's not like I'd be headed for a flight out of Zurich, that I had to catch! I can wing it. I'm just not sure how much winging I'd be doing! Course, it'd never be as much as I did last April, trying to get to Krakow from Tatranska Lesna in Slovakia, but I digress...ask me about that if you want a laugh! Thx. Tom

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