Somewhere between six months and two years, with the lower end of that range being more frequent.

I literally came up with this answer by finding a copy of John Ingamell's Dictionary of British and Irish Travellers in Italy, 1701-1800 and scanning through a couple pages of the entries, and seeing what trip lengths seemed most common. Ingamell's book has over 6000 short biographies of English-speaking upper-class travelers, including approximate trip dates. It's probably possible to statistically analyze this data to come up with a more precise and quantitative answer than the one I provide. However, I am not about to spend several days of my time hand-transcribing the dates and names in Ingamell's book into something machine readable.

That would actually be a great project for an undergraduate thesis, now that I think about it.