The last time that I reconnoitered with Goethe was (... some years ago), being assigned "The Sorrows of Young Werther" in a literature course. The highly romanticized account of love beyond the reach, culminating with Werther's taking of his own life, is not one that is easily forgotten.
Despite this biography's being is a weighty tome of some 600 pages, there is not too much in the way of first person accounts that would shed light on Goethe's NPA type. Thus, one has to assemble a picture from a variety of sources to arrive at a gestalt.
We do have the opinion of his colleague, Johann Kestner, whose fiancée was the object of Werther's (Goethe's) infatuation in real life:
"... Goethe has what one calls genius and extraordinarily lively imagination. He is intensely emotional... he has a noble way of thinking. He is a man of character. He is bizarre, and there are various things about his behavior and appearance that could make him unpleasant... He does whatever occurs to him without worrying whether it pleases others, is fashionable, or permitted by good breeding... He hates all constraints. He holds the female sex in high regard..."
Indeed, he did hold the female sex in high regard. From the early days as "Werther" to his old age, he was constantly smitten with young women decades younger than he, to whom he would unashamedly propose marriage (They would famously turn him down).
Goethe was something of a dabbler who did not realize when he was out of his depth. He challenged Newton's theory of light and spent many years promulgating his own fuzzy "theory of colors". He considered himself knowledgeable in the field of geology and collected thousands of specimens of minerals.
His handwriting was sometimes characterized by bold flourishes.
Not all of Goethe's contemporaries held him in high regard. When he died, a prominent literary magazine did not comment on his passing, as if it were not worth mentioning.
Our general impression is the Goethe was an N type.