I'm not a fan of that approach I must say. It's private property afterall and not the responsibility of those who own a holiday home to provide housing.Will disincentivizing second property ownership through a larger property tax not push more people to sell vacant or second properties helping the situation? It won't solve it obviously but could make some difference.
Also, most holiday homes (by their nature) are nowhere near places of high employment, so not sure how effective it would be if they came on the market.