If my business sale includes a rental building, is that building covered by the section 167 no-HST election too?

It depends on whether the rental building is genuinely part of the business being sold, or a separate asset that happens to be owned alongside it. The section 167 election covers the property that's reasonably necessary for the purchaser to carry on the same business, so if the rental building is itself the business, for example, an actual rental property operation being sold as a going concern, with the building at its core, it can generally be included within the election along with the business's other assets.

If, instead, the rental building is more like an incidental real estate holding that isn't really what the business does, and the "business" being sold is something else entirely, the building may not be treated as necessary property for that election and could be subject to its own separate GST/HST analysis, including its own potential exemptions or taxable treatment depending on how it's used.

Because whether a specific building falls inside or outside the election depends on exactly what the business does and how central that property is to it, this needs a careful, asset-by-asset review with a tax advisor before closing, don't assume a rental building automatically rides along with the rest of the business assets under the same election.