As currently specified, it sounds complicated, both to understand and to implement. So why not narrow the net of this tax, to just be about residential property. That will make assessment and collection easier, because it could piggy-back on council rate collection (just like GST piggy backs on existing transactions, to obtain calculate its amount and obtain a channel for payment).
Narrowing the focus to Imputed Rents also greatly reduces the burden on TOP, in terms of explaining and justifying this tax. Yes, there's the unfamiliar concept of imputed rent, to explain, but that has to be explained no matter how this tax is formulated. The problem is, that if the tax is formulated more widely than residential property, then the burden of explaination becomes much greater. E.g. if it applies to a luxury car, is that on the basis that its a tax on the amount you would pay if you rented a similar car? Or is it on some other basis? And what about how this applies to businesses, the concept of imputed rent doesn't really seem to work as an explaination for why this tax would apply to them.
All in all, it seems much more likely to be understood by the public if it is collapsed down to just a tax on imputed rents. And that's its best chance of success, IMHO. Of the people who understand it, I don't know what percentage will support it. But I'm fairly sure that, of the people who don't understand it, virtually none will support it.
The reason is because a major objective of the closing of the loophole in our income tax regime is to target the way businesses deploy their capital, namely to increase productivity. If you have a business that year after year makes lacklustre returns on the capital it owns, then that capital needs to put to work more productively - either by the existing owner utilising it better or by it being sold to someone who can. Productive capital is a scarce resource, this policy will raise the supply to those who can get a return on it.