I think, the confustion stems from the following.
One assumes, that 66 model refers to Levis 501XX made in the year 1966 as a blue print.
Howeve it seems, that the definition is that the 501s produced from 1973 to 1980 are referred to as “66”.
The name comes from the fact that “© 1966” was printed on the flasher.
The 66 model is again subdivided into first half and second half models.
Same same, but different is the Big E- model.
This refers to the 501s produced from the late 1960s to 1973.
After the Big E the red tab showed “LeVI’S”.
Also the lot number was changed from “501XX” to “501”.
According to this Japanese Denim somelier "mtk0058" among others the v stitch at the top button was used until 1969 and the parallel stitch from 1969/1970 onwards.
There were also changes in the arcuate stitch colours and a switch from from back pocket hidden rivets to bartacking.
So, I guess, when a 66 model is offered it can be one with Big E, first half 66 and second half 66 characteristics. And the cuts were probably also changing over the years.
Clearest would probably be the following three models:
1. Big E with parallel stitches 1969-1973
2. 66 first half model and
3. 66 second half model
There are probably other theories about this. But this is the info I had found on the insta of mtk0058 and in this article.