The word זיז occurs three times in תנ”ך.  Twice it refers to some sort of creatures, in the expression זיז שׂדי.

The third occurrence, in Isaiah 66, clearly has different meaning.  The context is a metaphor comparing the consolation of Israel in it’s redemption to nursing from the “breast of consolation”.

Rashi understands זיז here from זוז, to move, and explains מכבוד גדול הזז וממשמש לבא לה, and then translates זיז into Judeo-French as אישמובימנ”ט – which Katan explains as esmovement.  Targum Yonatan translates as מחמד, and רד”ק writes in accordance with Targum Yonatan that זיז is like זיו.

Chaim Cohen, in his PhD dissertation Biblical Hapax Legomena in the Light of Akkadian and Ugaritic, points out that a similar word in Akkadian (Ugaritic?) means breast.  (He points out that was was first recognized by Strong.  See Cohen’s footnote 217.  Cohen writes “[t]he context of the Akkadian passage makes this comparison virtually certain.”

Incidentally, Cohen points out that there are two hapax legomena in this verse, תמצו being the other.