PN3...
I've often wondered the same thing. I've heard anecdotally—and possibly apocryphally—on this site that the PN3 was a variant of the PN2, used for Electrolux's commercial vacuums of the era. The '3' supposedly refers to a third ground lead, which would have been required for commercial applications. Of course, that begs the question of whether anybody has actually seen one of these beasts in the wild.
For what it's worth, I really like the PN2's refined design far better than the very similar PN4/4A, which seems to have fallen victim to sacrifices made for manufacturing efficiency at the expense of performance. Although all PN2s had beautiful polished aluminum cases, there are two minor color variants of the PN2: teal or white necks with color coordinating rollers underneath. The teal necks are the earlier variant and would have been included with the 1205s, although I have seen some with 50th anniversary stickers on them, indicating they would have shipped with the Golden Anniversary 1205s. The necks switched over to white during this 'golden' era and would have been shipped with the aforementioned golden anniversary models as well as early Super J machines. Later Super Js shipped with polished PN4s, as did some early Olympia One units before they made the unfortunate decision to start painting them chocolate brown and then Silverado gray. The PN5 "Omniflow" power nozzles were introduced late in the Silverado's run.