Are you fucking serious??
Because of recent changes to council tax, people are making the really hard decision to sell family homes. Yes they are second homes, but family homes too. The owners have contributed to local economies for generations. They have held onto those homes while paying inheritance tax.
You want local people housed. Let's get real: jobs are thin on the ground in holiday areas, and most of the jobs in enchanting but remote touristy areas don't pay well.
There's a reason why there's a slump in the market for homes in "holiday hotspots" (coastal/highland/picturesque). It's the extra council tax on second homes that's either already been imposed or is on its way soon.
But even with the current dip in the housing market in holiday areas, and even though owners/renters of a single property "only" have to pay the normal amount of council tax, house prices are still too high for many: young people, young families.
And so almost all second homes, in Cornwall, Pembrokeshire, wherever, will be sold not to locals but to new second home owners. "Old school" second home owners selling to new money second home owners is, and will be, to the detriment of the local economy.
Buyers in the market for a second home are more cautious now, unless, as I said before, they are very rich indeed. So sellers who are parting with places dear to them are already having to settle for less than what the market value would be without the caveat of huge council tax.
But now you want the sellers of second homes penalised with an extra tax, a "local Stamp Duty" for selling to "the wrong people"? You want them to sell to local people only?
Then you fucking step up, via your income taxes, and massively subsidise the local buyers in holiday areas, so that they can afford to buy a house.
Step up and pay more income tax towards building more social housing. Pay a "local Stamp Duty" yourself, should you be judged to be selling your home to the wrong kind of people.