Working at an embassy of another country in Japan

Hello, writing from a throwaway account because of shyness.
I have been living in Japan for a couple years now, nowadays I have the 技術・人文知識・国際業務 Visa and I have a very good chance of starting working at the embassy of a country that is not the country I am from, in Tokyo.
The thing is, when I asked them about the visa problem they could not answer the most important question, if I was allowed to work at an embassy of another country in Japan with that status of residence. I do not want to do the whole process just to be told that I can not work with them because of my visa, does anyone know about this or about 公用 visa? Thanks.

Just to add, I am a 専門学校 graduated, I do not have a bachelor.

by ApprehensiveConcept