I am sorry, but nothing you are saying makes sense to me. Shining lights thru; If you see "kernels", it sounds like a cultured pearl necklace. Purchased in the 60's sounds like it is cultured also. The sizes are of a typical akoya necklace of the 1960's, The place of purchase does not indicate they are natural. In fact, jewelers hardly ever have natural pearls for sale; they just can't get them and they cost too much. Jewelers rarely know anything about pearls. Their word can't be trusted when it comes to natural pearls- most of them have never seen a natural pearl.
I need to know if we are having language issues. Do you understand what I mean by "real", cultured" and "natural"? the new photos don't help either. the light on the right is too harsh to see anything about the quality, the one on the left is on a very busy background even though it is white. Would it be possible to take more photos on a plain white paper towel, in indirect light with more close ups including the clasp?
So far, your necklace looks real. It looks like a cultured akoya necklace.