To add to my previous rant, Overseeing in Anatolia, it turns out that a quick google search yielded a gem in my favour. To recap, since the attested Etruscan words zilaθ and zilχ strongly imply a verbal root *zil- presumably meaning 'to oversee, to supervise', I considered the possibility that the verb was simply inherited from a Proto-Cyprian form *zila-. I then considered the possibility of a relationship between this word and Hattic zilat 'throne, seat' by way of a cultural exchange between these two unrelated language groups. I asked: Could this latter word be built on a Hattic verbal root -zil? Is there a shared verb pertaining to governance between Hattic and Cyprian? Sadly, Cyprian-Hattic loans seem to be hard to examine given the gaps in present-day linguistic information of that region and time period.
Now to the aforementioned gem. I came across Yasemin Arikan's article, An official in Hittite cult: LUtazzelli-, where he surprisingly contemplates precisely this Hattic verb, *-zil, but with the added evidence of another Hattic word, *ta-zil, pertaining to a type of official. If I understand correctly so far, ta- creates derivative nouns as in *ta-parfasu (cf. Hittite taparfasu-, a type of ritual bread), and another noun *t-astup (cf. Hittite tastuppa-). Both of these latter nouns are mentioned in Petra Goedegebuure's article I read previously.