Let's talk about the notion of a "finite verb" in Etruscan.
From what I understand thus far, Etruscan has two tenses: past and non-past (aka present-future). So given a verb am 'to be', the past tense is ame 'was/were' (-e for past tense) and the present-future tense is ama 'am/is/are' (-a for non-past). We can further elaborate on these verbs with additional aspectual markers like -ac- for the perfective, thus amace 'has been'. I have yet to find evidence that the Etruscan language had any markers of person, so these verb forms might very well have been used for any person, singular or plural, in the same way as Japanese tabemasu 'to eat' is likewise completely unspecific for person or persons.
This brings us to the topic of finite verbs in such languages. According to Richard Norquist's definition of a finite verb, it is "a form of a verb that shows agreement with a subject and is marked for tense." Yet, as I just wrote above, it may very well be that the Etruscan verb, as in Japanese, never agrees with the subject because it simply lacks personal markers. As such, I gather that the difference between finiteness and non-finiteness in the Etruscan verb relies strictly on the presence or absence of the meager tense marker in -e or -a. This difference then is so slight that there are cases where it appears that Etruscans freely reincorporated non-finite forms, even noun stems, into finite verb forms with the simple addition of tense markers, creating some interesting derivational complexity in the process. An example of this liberal agglutinative process may be seen, for example, in the form trinθaśa attested in the Liber Linteus (LL 7.vi), built on a stem trinθ, a tenseless mediopassive participle, in turn derived from the mediopassive trin (LL 7.iv), derived yet further from its fundamental root, tra 'to pour' (hence its own transitive participle trau as witnessed in LL 4.xxii, 9.xxix).
This language never ceases to amaze me in its simple rules but brilliant sophistication and communicative freedom.