The choice of ending is somewhat arbitrary (well, in theory the tradition informs our modern chant editions, but that's another question), because the Roman antiphonal (or antiphonals, rather, because there's the pre-conciliar version and a new, post-conciliar one as well) has fewer endings than the monastic equivalents (for the main Order of St Benedict, that is).

Ordinarily, the termination leads us back to the first note of the antiphon, hopefully in the most melodic and convenient way. Sometimes it's the same note, e.g. 8c leads us back to Do, the first note of an antiphon of mode VIII in this family.

There are not all that many mode VI antiphons, certainly not in the Roman repertoire. I thought of three (two Magnificat antiphons, one for a psalm) from the ordinary cursus (O Admirabile commercium, from the Circumcision and Candlemas; Serve nequam, from the 21st Sunday after Pentecost; O quam suavis est, from Corpus Christi;). They all begin on the same note: Fa, or in the third case, Do, because it's transposed. I would hazard that there are in fact no other first notes: it's always going to be Fa or Do, but I could be wrong; if I am, then it's a first note that would permit one to easily get back to the first note.

That said, some of the endings don't seem to be for anything but variety because it moves us away from the first note of the antiphon, e.g. the variant endings of 8G in the monastic antiphonal; there is the usual 8G that ends just on Sol (this is the ordinary version, then 8G* that gives you Sol-La, then I believe it's 8G2 which is Sol-La-Sol; I'm never sure that 8G* is easier to sing in conjunction with the antiphon compared to the other two endings (but if it's says 8G*, I use that ending despite my doubt), whereas I think that 4A and 4A* (ending on La and then on La-Si respectively, as this version of mode IV is transposed and in some editions is replaced with mode II transposed) tends to be a hard ending to sing but that La-Si makes returning to the reciting tone and the first note of the antiphon easier; that's in my very humble opinion. Solesmes family apparently didn't agree, or at least Dom Suñol of Santo Domingo de Silos didn't back in the 1920s.

I wish that I knew how to do such things! But there we go: out of the Do antiphons, surely some are transpositions as we see with Serve nequam, and then we have a descending minor third or half-step, which are easy to navigate from Fa.

@MatthewRoth Thank you so much! It never ceases to astound me how deep the rabbit-hole goes with any Gregorian Chant question! And it is continuing to dawn on me just how much the Antiphoner governed the Offices musically. I just had no idea. Thanks again!

@MatthewRoth All the tone VI.F Gregobase antiphons beginning with Do turned out to be versions of Quo abiit (just minor melody variants for the same lyrics).

And the mode VI melody doesn't seem to be ancient.