What disincentives could discourage people from buying second homes?

There are areas that have banned second home ownership. It really does need a centralised approach. There is also the issue in big cities of overseas investors buying up loads of properties. I would ban non-dom's from buying new properties. Anyone who emigrated should be able to keep their property.

Quadruple council tax, proceeds of which are pumped into the community

I'm not sure disincentives are what's needed- by definition second home owners are rich so financial disincentives have limited use, and the idea of authoritarian rules about who is allowed to live where is abhorrent.

The solution is more fundamental- investment in infrastructure in the regions and incentives for businesses to be based throughout the country, not just in cities (and London in particular). If we want thriving villages, we need good employment opportunities throughout the country rather than concentrated in a few smaller areas. Simply removing the second home owners won't bring back local schools and buses if there aren't opportunities locally for the people who might live in those houses instead. You just end up with properties standing empty.

I have seen it in action where we live in rural Suffolk- the energy coast. There is a huge amount of money being spent on infrastructure and energy assets, which has brought great employment opportunities across a wide range of roles, which in turn means opportunities for businesses serving those people- a virtuous circle. This is in part of the country where we've previously had lots of issues with loss of services due to both second home owners and abandoned houses, because there simply weren't jobs for people to do outside farming/casual labouring.

Locals could stop selling the houses to them.

Alternatively ramp up stamp duty and council tax even further

Maybe a law that says any property must be inhabited 6 months a year or suffer a penalty? That might at least make people split their time and contribute to the community? Empty or near empty properties are shameful when there's a housing shortage, which forces us to destroy more natural habitat to build more houses.