It does seem that ITO was a separate company to ITO-YA, and was responsible for the pencil in the original post. I have a set of ITO technical pens with the same logo as seen on the pencil clip, which the box attributes to ITO & Co, Ltd.
Whether ITO was the actual maker is unclear, as I have another pen set with the very same pens, but this time by Sakura:
If Sakura was the manufacturer, is it possible that they also made pencils for ITO? I also noticed that the tail end of the ITO pencil is very similar indeed to these Gakken pencils (fourth and fifth from left in the top photo), but with a fixed clip.
It does not surprise me that ITO was also an office furniture supplier. This seems to have been a common fate for drawing instrument manufacturers, such as Riefler in Germany and British Thornton, both reinventing themselves as office furniture businesses after CAD killed off the technical drawing market (British Thornton finally went out of business in 2020).