So the uses of the word TAXIS when not plural has an entirely different meaning that the singular TAXI.

There are two different words, with different etymologies, that you have combined. The Greek taxis 'arrangment, order' and the German family name, which in turn is from an Italian aristocratic family Tasso, which means 'badger'. The -s in the Greek word is not a plural ending. It is a nominative singular one. The -s in the family name is anybody's guess as it was not there in the Italian original. The etymology is mentioned in the Wikipedia article you've linked to also, but i have read it in other sources, and it is a reputable one.

Ceci n'est pas un seing.