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> but I don't think I can count on that working

There really doesn't seem to be a ready-to-use way to get that message (which feels like a good feature-request).

While `ex.args[0].args[-1]` is indeed not robust, you could make an error-processor that uses `isinstance` + `getattr` + ... to handle more cases; something like this:

    def exc_to_message(exc: Exception) -> str:
        reason = getattr(exc, 'reason', None)
        if reason:
            if isinstance(reason, bytes):
                reason = reason.decode('utf-8', errors='replace')
            return reason
        if exc.args:
            arg = exc.args[0]
            if isinstance(arg, Exception) and arg is not exc:
                message = exc_to_message(arg)
                if message:
                    return message
            # fallback 1
            return str(arg)
        # fallback 2
        return str(exc)

which is more a proof-of-concept than a complete solution; I think a better solution would require changes in urllib3. Just getting a clear "connection refused at {host}:{port}" right now would require regexes.