My main issues with vacancy taxes are three-fold:

1. The cities with the worst housing crises are typically the ones with the lowest vacancy rates. This makes sense, as if vacancy rates are super high, potential tenants have a lot of negotiating power against landlords, so they can demand lower rents. When there are very few vacancies relative to the number of prospective tenants, landlords have all the negotiating power and can demand high rents.
2. Vacancy tax focuses on shuffling ownership of existing units and doesn't do anything to encourage densification and development. Own a detached single-family home right next to a metro station in the middle of Manhattan? So long as someone lives in it, you pay no vacancy tax, despite the fact it's clearly a massive waste of some of the most valuable land in the world.
3. It's easier to evade and thornier to implement. For instance, there are a lot of "statistics" thrown about regarding "millions" of vacancies, but many on-paper vacancies aren't what you or I imagine. For example, "vacant" technically includes student apartments where the student lists their parents' address as their permanent address. Getting back to the point, if you can just on-paper claim a unit is occupied, you can evade the tax, which means the government then needs to actually go out and check if someone us actually living there at least 180 days out of the year, which is way harder to enforce.

Altogether, vacancy taxes are a pretty marginal solution, and I think our focus is much better spent on land value taxes and YIMBYism (e.g., zoning reform).

A 2nd property should be taxed at a higher rate regardless.

This can probably answer your questions.

A key idea of land value taxes is it's on land value, rather than land area. Urban land is faaaaar more valuable than urban land on a per-acre basis, so someone who owns 1 acre of land in Manhattan will pay vastly more than a farmer who owns 1 acre in rural Nebraska.

As for appraisal, we already sorta do this with property taxes, as property taxes tax the land value + improvement value. With land value taxes, we simply seek to tax just the unimproved land value. Why? Property taxes can disincentivize development and incentivize land-hoarding and speculation. In contrast, even a milquetoast land value tax has been shown to reduce land speculation.

Okay but farmers already get so many subsidies that it wouldn't at all be hard to write exceptions already built into the lower for them? Hmm.

What about Henry George, then?

Henry George (September 2, 1839 – October 29, 1897) was an American political economist and journalist. His writing was immensely popular in 19th-century America and sparked several reform movements of the Progressive Era. He inspired the economic philosophy known as Georgism, the belief that people should own the value they produce themselves, but that the economic value of land (including natural resources) should belong equally to all members of society. George famously argued that a single tax on land values would create a more productive and just society.

I'm not a fan of sales taxes, because they tend to be more of a burden on the poor than the rich. I much prefer a marginal income tax to that.

Personally, I think our philosophy of taxation should be "tax what you take, not what you make".

Because there's finite land on Earth and nobody has created it, you occupying any parcel of it necessarily denies others from its benefit. Hence, a land value tax in proportion to the value of land you have taken from the rest of society.

Similar for finite natural resources. There are finite mineral deposits, finite oil deposits, finite phosphate deposits, etc., and anyone who extracts them takes something from the rest of society. Hence, we ought to have a severance tax in proportion to the value of the resource you have taken from the rest of society.

And also similar for negative externalities. When you pollute a river or the atmosphere or cause any other negative externality, you are forcing those around you to bear some of your costs, that is you are taking value from them to give to yourself. Hence, we ought to have externality taxes (aka "Pigouvian taxes") in proportion to the amount of harm you have caused to society.

Further, I think taxing along this principle leads to the best overall outcomes, not just from an abstract sense of "fairness", but from pragmatic economic outcomes.

Take land value taxes: economically speaking, LVT is just a great tax with great properties that has seen great empirical success.

Or severance taxes: Norway has used them brilliantly to solve the resource curse.

Or Pigouvian taxes: basically all economists agree carbon tax-and-dividend is the single best climate policy.

But yeah, absolutely everything else should be tax-free. The government shouldn't even be tracking your income, much less taxing you on it. Tax the land hoarders and polluters instead.

This will do the opposite of what you want. All of these policies disproportionately cause poor people to remain poor.

It's not intuitive and it sounds great till you realize that unless you tax wealth and income with a progressive rate well into the 90% at the highest levels.

People who are wealthy don't give a single shit about consumption tax. They also don't care about transaction taxes (unless it's progressive). A person with a million dollars doesn't care if milk costs 5 bucks or 6 bucks a gallon... But the person making the minimum wage absolutely cares.

Sales tax is deliberately regressive, taxing the poor more than the wealthy. Why would you have it, rather than income tax?

http://gameofrent.com/content/can-land-be-accurately-assessed

The key downsides of income taxes, though, are it requires tracking everyone's income, and it's very easy to hide income by doing under-the-table work and getting paid in cash. In contrast, it's impossible to hide land.