Some models were given no tool box. Instead, the tools were wrapped in a roll-out pouch with two ties like shoe laces. I've hunted the web looking for such item, but not found. The Japan Tractor History Museum only mentions this with no images.
When you see a parts manual with just the tools show, they are typically wrapped in the pouch.
My guess it's sort of like this,
The models in YMxx
20 received several upgrades and options. These models received the red full sized tool box.
Here we see the YM2620 with the toolbox mounting flanges and holes.
The mounting behind the seat continues from the larger YM models into the F and FX series.
When I went searching for a useful tool box, I picked the YM2620 size.
I got one for free from another Yanmar owner who blessed me with it for all the help given to others on the tractor sites. It was still the red faded color for being 40 years old.
After clean up, primer and then Yanmar red, it looks beautiful once again.
Here is an early Yanmar FX machine with OE tool box.
When these machines are export out of Japan, many of the tool boxes are removed and tossed.
For the extra 2 or 3-lbs to fill a shipping container to keep them for a dozen machines, I don't understand why they are tossed away.