I'm curious to know if anyone has any information on the 13ZN non-flyback models.

Here is one recently sold at Phillips;
https://www.phillips.com/detail/LONGINES/CH080216/176

 

...I don´t know why, but they built some without flyback.

Furthermore the early ones:

and the 13ZN12 which is on principle without flyback.

 

this is actually a very good article on Hodinkee re: 13ZN that I quite enjoyed reading some time ago:
https://www.hodinkee.com/articles/longines-13zn-history

 

The non flyback can be easily spot just looking at the dial which is an easy way during research
I line the non flyback dial... Really simple and that's it!

 

If you are accurately measuring time for the purpose of measuring time, non-fly back makes it idiot proof that you won’t accidentally reset the time before noting the elapsed time. Like for artillery or racing use, basically not pilot use.

 

I noticed they were all delivered to Switzerland during war time.