For industrialisation, you also need certain resources and knowing what your economic strong suits are.
For example, would it make any sort of sense to focus on heavy industries in southern Italy ? Resource-intensive industries might not be the answer, especially if coal, iron ore, other metals, etc., are hard to acquire in the region itself. If you need to import iron ore and coal on a regular basis, that demands a lot of big infrastructure (factories, railways, freight ports, coalyards, ore storage) and makes it unlikely for steel mills to be located more inland, beyond the seaports. Or, on the off-chance, outside of the better rail-connected cities.
Would light industries make more sense, combined with commerce, smaller enterprises and investment into areas where local resources could be used and reused reasonably ? Developed food-processing industries, industries focused on pottery wares, in later eras maybe chemical and pharmaceutical industries... Precision industries that can utilise off-the-shelf metal (or later plastic/polymeric) products. You could maybe even start a timber industry. Have the southern governments start pursuing a policy of reforestation in the last two hundred years, wherever possible and effective. Set aside some forests for true rewilding (maybe a third) and the rest (maybe two thirds) for fairly sustainable logging practices (i.e. not exactly tree plantations, but economically-focused forests usable for the timber industry). Construction industries are another possiiblity, though with a potential for issues or corruption. Overfishing and overgrazing could become concerns in a food-production-and-processing focused industry, so this also needs to be taken into mind, and soil issues due to weak or bad land management could also cause losses in agriculture, especially one geared towards the food-processing industry.
As others have noted, investing into education and human capital is also a real boon for expanding industrialisation, as you're more likely to have an educated populace that can either provide expertise for industries (in theoretical knowledge and manual labour skill) or start their own small and medium enterprise that becomes part of the wider economic modernization (since the 19th century, or even sooner). We often think the early industrial revolutions were only about illiterate and poor labourers toiling away like slaves, but the growing effectiveness of modern industry went hand in hand with improving education standards, people empowered to do business or earn a reasonable wage. And later on, health and safety issues being taken far more seriously (this becoming more prominent in the last one hundred years, 19th century standards in these areas being more lax, though not universally everywhere).
Improving infrastructure to start a proper tourism industry a bit earlier would be a pretty big asset, I feel. Might make the place tourist trap-y far sooner or far moreso than in OTL, but it might bring in some bucks, hopefully without too much cynical disruption to local historical and cultural heritage. Improve the road, rail and ship connections and you might see tourists visiting the wider region on a more common and more organised basis.
Another service sector option even in the 19th century is going the Swiss route and providing international banking services. Obviously, this area has a huge potential for corruption issues, and financial services aren't exactly industrialization, but they could start to accumulate some degree of wealth from hard-paying clients.
Even with an industrialised southern Italy, and with the service sector (tourism, hypothetical banking) added in, I still have to wonder how this would affect or change the long-standing tradition of organized crime in southern Italy. In an industrialized version of the wider region, we might not get rid of gangs and mobsters, but they might develop into something different, maybe more akin to organized crime in other European countries that underwent industrialization.
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