I could be mistaken about this, but I don’t think the Apple 2 can see if “blink” is working or not, it’s a video hardware attribute that makes character cells with a value set between 64 and 127 invert or not based on the state of a 555 timer circuit with a roughly 2sec interval.
Does the diagnostic program test the available attributes (normal/inverse/blinking) and that’s fine but only the cursor doesn’t blink, or is reverse and/or blink never working? You could test this in BASIC by directly poking the text screen buffer.
This stack exchange post has a list of the attribute mapping. I will note for completeness sake that if the II+ has a lowercase mod it may affect things.