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I looked at the packaging tests (thanks), but I didn't find anything useful to me. There were a couple whose names looked promising, but they turned out to be stubs. As far as I can tell, none of those tests actually invoke the system's C compiler, even indirectly. They are numerous, however, so I could have overlooked something.
It occurs to me that because the extension only needs to provide one function, I could just add that to _tkinter. That would ease testing without adding anything to the *public* API, but it seems a bit smelly to me because the point is that a user extension can trigger the bug. Also, the added function would be accessible to programs that choose to ignore privacy convention.
Also, I am assuming that tests only need to be runnable by developers and build automatons -- i.e. someone who can and did build Python from source. If they need also to be runnable by end users then a compiled version of any extension the tests depend upon needs to be included in binary distributions.