This is going to be a little more nuanced and probably something that I cannot give you a definitive answer to on the forum (because it deals with local tax laws that require review of the local codes which are usually not published online).
However, what I can do is help provide you with the tools to investigate this and address it yourself.
The tax code (like any other rule) must include the appropriate determining factors for taxing the properties in the rule itself (if it isn't written down, it isn't enforceable).
So going to the specific tax code that they are attempting to levy this school tax with is going to be the place to start.
Once you are there, you can identify whether the code section itself has any guidance.
If it does not, then you can work backwards - go to the code chapter (or section heading) that it is in. There will be terms and definitions that provide information that give guidance on how to interpret the sections themselves.
(For something like a school tax, I can tell you that a rough "rule of thumb" - so not a statutory rule of interpretation, just something to help simplify this particular tax - would be "if you have children living at the property, and they were enrolled in public school - if they are attending the school where the school tax is being levied - you owe the tax")