When to use private interface methods over private static methods?

Question

For Java 9 and on, I understand that private interface methods can be declared and implemented in the interface, then called by default interface methods (of the same interface).

But, private interface methods cannot be called by static interface methods.

Now, I also understand that private static interface methods can be declared/implemented in the interface, then called by default as well as static methods.

So it seems to me that the abilities of a private static interface method is a 'superset' of a private interface method.

If that is the case, is there any situation where using a private interface method is preferable to using a private static interface method?

For example:

public interface Schedule {
    default void wakeUp() { checkTime(7); }
    // static void sleep() { checkTime(21); } // compile error if private interface method called
    private void checkTime(int time) { // if so, why not always use private static method instead?
        // implementation omitted
    }
}

Answer 1

A non-static method can itself call other instance methods.

public interface Schedule {
    LocalTime getCurrentTime();

    default void wakeUp() { checkTime(7); }

    private void checkTime(int time) {
        if (getCurrentTime().isAfter(/*something*/)) {
            // do something
        }
    }
}

If it were static, it couldn't do that. If you don't need to call another instance method, make it static.

This is pretty much the same logic you should follow when writing a normal class.