When is it acceptable to declare an instance attribute outside "__init__()"?

Question

I will start by describing the dilemma I'm currently facing. I've a class (let's call it NeatClass). It has several instance attributes, all of which I declare, as usual, within the class' __init__() method. I'm adding a new method (let's call it util_method()) to the class and it requires an internal state to be kept between calls. My intention is to store that state in an instance attribute (let's call it self._util_attr).

Now, according to the "usual guidelines", I should declare self._util_attr inside NeatClass.__init__():

class NeatClass:
    def __init__():
        self.attr1 = ...
        self.attr2 = ...
        # ...
        self._util_attr = None  # type: ignore

I understand that declaring instance attributes inside __init__() is supposed to increase the code's readability (see this and this SO questions) - I totally agree with it. However, in my use-case, doing so might have the opposite effect. Here's why:

• In my class, only util_method() is supposed to use self._util_attr.
• Although I want util_method to be part of my class' API, it will only be used in some rare occasions (most instances of NeatClass won't use this method at all).
• I'm using mypy to type-hint my code. During the call to NeatClass.__init__(), the type of self._util_attr isn't known (hence the comment # type: ignore). For reasons that are outside the scope of this question, I can't use Union or something like that to type-hint this variable.

So, what I really want to be doing is this:

class NeatClass:
    def __init__():
        self.attr1 = ...
        self.attr2 = ...
        # ...

    def util_method(self):
        if not hasattr(self, "_util_attr"):
            self._util_attr = ...  # initial value of the variable
        # ...

However, I want my code to follow both PEP8 and Google Python Style Guide. So, I searched both guidelines for references to situations in which declaring an instance attribute outside __init__() is acceptable. As you might have imagined, I didn't find anything. As a matter of fact, I didn't find anything about "declaring instance attributes inside __init__()" at all, which really came as a surprise. This lead us to my question:

Are there any situations in Python's common style guidelines (especially PEP8 and Google's) in which it is acceptable to declare instance attributes outside __init__()__?

Pointers to where, in those guidelines, it's specified that instance attributes should only be declared inside __init__() would also be appreciated. Also, suggestions on how to refactor my code are welcome.

Please note that I'm not looking for opinions (which, in turn, would violate StackOverflow's guideline). I'm simply looking for references to sections of Python's most common style guidelines that address the situation I described. I also don't think this question is a duplicate - I've read several other SO's questions on the subject and none of them seemed to be asking the same thing I'm asking here.

Thank you for your time!