Here's a funny thing, in the UK the main tax associated with owning a house is council tax, you pay it to the local council for the services they provide (although we can have an argument about where the money actually goes since it's all fungible anyway and the central government repeatedly butts in and restricts councils). As you suggest we could disincentivize second home ownership by levying a higher tax on it.

How does this manifest in real policy in the UK today - 2nd homes, and homes occupied by only one person more often than not receive lower taxes than normal.