Maybe the way I wrote the replies or the article was confusing. I do own two of them out of the twenty known. One of the easy way to tell is with the Japanese writing on the back of the Weems which you saw. There is another way to tell, which is by the order number inside the case. 20853 is only for the Japanese Navy. I own #946 and #832.
Front of the Longines 832 and 946.
This is 832 from outside.
Here is a good image of 946. You can see the Japanese stamps from the inside the case.
This is 946 with a Data Plate from a A6M2 Mitsubishi Zero Zeke
The aircraft serial number was 2302
The watch is in John Goldberger book on Longines.
The Weems is mentioned here in this book on Japanese military watches.
It says dome of them were ordered by Tateyama Imperial Japanese Navy Base.
And here is one of the Weems at the Tateyama Navy Base today on display in their museum.
To buy one, I had to first find out who owns one. So for half a year, I found all that exists.
And there is another one currently up for sale on Chrono24.com for a good price. Not expensive for one of these rare birds.
Picture I took from a WW2 new reel film. Reconnaissance pilot definitely looks like he is wearing a Weems.