I've found two possible etymologies for this:
The Book of Song, in which the Emperor of Japan basically asks the Chinese Emperor if they can borrow the Chinese language for a while. (不動 is used within the letter)
and
大道無形 Daidõ mugyõ, The Great Tao is without form, 眞理無對 Shinri mutai, The Absolute is without opposite; 等空不動 Hitoshiku kû fudõ, It is both empty and unmoving, 非生死流 Shõji no nagare ni arazu; It is not within the flow of Samsara; 三界不攝 Sangai fushõ, The Three Realms do not contain it, 非古夾今 Koraikon ni arazu. It is not within past, future, or present.
Nan-ch'üan P'u-yüan (Nansen Fugan 南泉普願) (The Development of Chinese Zen After the Sixth Patriarch 58)
The Japanese pronunciation of a Zen poem about the Tao.