When re-reading Jean-René Jannot's last book Religion in Ancient Etruria (2005), I continue to feel that he's grasping at straws, muddling his way blindly through the murky waters of both Etruscan language and religion, not firmly understanding either. In this respect, it would appear he is merely a typical Etruscanist who sells mystery and hearsay in place of diligently researched facts. On the curious deity Tecum which is found inscribed on the Piacenza Liver he writes on page 147: "The sector after Uni's (no. 5) bears the inscription tec/um. Could this be one of Menrva's names - one linked to her cosmic function?" As I've remarked before, this book is riddled with errors of various kinds (see Paleoglot: Religion in Ancient Etruria: A comedy of errors that keeps on giving), too many for my liking. (Here too the inscription in question should have been more accurately written tec/vm with digamma transcribed properly by 'v' instead, as one can see with the available photograph below on the bottom right portion of the border. Fortunately, it's only a minor detail this time.)
First, if we must squeeze out the Capitoline Triad from our analysis of the Piacenza Liver, Cilens-Tin-Uni seems a more apt solution since at least from this we obtain a more aesthetic symmetry when Uni and Minerva (as Cilens) flank both sides of the three aspects of Tin. In effect, a triad within a greater triad. On the other hand, there's nothing showing outright that the specific Capitoline Triad as Romans knew it must be present here in the first place. At any rate, that still leaves us with the nagging mystery concerning the true identity of Tecum.
Personally, I'm a fan of linguistic analysis as a valuable tool in helping to solve these kinds of mysteries. The Piacenza Liver is a bronze object designed to express the entire science of divination into a single model, uniting the practices of divination from lightning and bird omens (nb. the border representing the horizon and associated deities which is useful for these practices) with that of omens read from sheep livers (nb. the inner portion useful only to haruspicy). So it seems reasonable to presume that, where it regards the specialty of divination, notoriously considered Etruscan by even fellow Romans who employed Etruscan haruspices, there should be few if any xenonyms for the native Etrurian pantheon. That is, it would be rather unusual for an otherwise native practice to be riddled with names of foreign Roman and Greek names, wouldn't it? So as such, if we take Tecum to be a native name, the name then may unclench its secrets under our linguistic analysis and give us a hint as to this deity's underlying function.
Finding a root in this name is a cinch, which can only be the verb tec as seen in its simple preterite form tec-e (TLE 651). The remaining is a suffix -um which is fortunately attested a few times in what appear to be abstract, uncountable derivative nouns expressing concepts of mass or material as in meθlum 'people' (from *meθil 'group') and vinum 'wine' (from vina, also 'wine'). In TLE 651 where we find tece in the sentence Auleśi Meteliś, Vel. Vesial clenśi, cen flereś tece, its most sensible value must be something along the lines of "erected" or "set up" since its accusative object (cen flereś) refers to the bronze statue on which this inscription is inscribed.
So given these facts, is it too unreasonable to deduce that Tecum literally means 'Firmament' and thus 'Sky'? Could it be that Tecum represented the vault of the heavens perchance? I hate to brag but this idea, whether correct or incorrect, beats randomly assigning Tecum to Minerva based on a package of whims.
 We might also analyse tece as a past perfective if indeed a syncopated form of earlier *tecuce.