FOUND IT!
Here is the beast! I'm including the unsaver and its possible variants as well:
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This wonderful PDF also has tons of information on the variants possible for the IBM unsaver:
The two attached PDFs will be:
1. The whole PDF that this came from.
2. Just the relevant pages, compressed to save space.
It's worth mentioning that the attached big PDF, has a list and lots of information of all the functionality of any terminal that can be connected to an IBM 3270 (like the 3290 Information display, which is only a dumb terminal that connects to the 3270) It is legitimately the most keyboard centric IBM manual I've ever read, and may provide tons of info to others who wish to learn more about that system as well.
TLDR: The unsaver side keyboard comes in a few form factors, including programmable function keys as well as varying numpads for different countries of the world, as well as one for the US market that does have a single double wide key. Realistically we are looking at the Programmable function keyboard on the picture in the Opening Post. I'm so happy I found this, I hope it helps someone down the line. In addition I found a ton of information about what different layouts an IBM Unsaver 104-key Model F can have, some of these may have never been seen in the wild, but now we have documentation that they were at least written about, if not manufactured.
The 3290 station that this was made with was very expensive and had tons of features, so many that IBM STILL has manuals from 2013 at the latest that I've found that explain how to connect that station to a Z/OS Mainframe. It seems that somewhere there is still some guy burning his retinas with the wonderful IBM orange plasma glow.
Let's hope he's not sitting on one of these cool keypads and keyboards.