What about their Europe-wide televised Rockpalast live gig on 19 April 1980? That established them in Germany and it was when they were still playing real trio music without backing tapes and drum machine enhancement. (Oh, I just saw that Rob made the same point. OTOH a filmed live gig is not the same thing as a live performance in a TV studio environment, those can go horribly wrong as they obviously did here.)
For me, ZZ Top peaked with Degüello (released 1979). I thought their 1980ies era gimmicky.
And btw: Trapeze want their 1974 riff back and played at the proper speed (at 00:18):
As for the Carson clip, the horn section was obviously under-rehearsed and missed a bar or two, not knowing where it was. Shit happens. The band was surprised and on TV not confident enough to actually wait a bar or two out to have everything in sync. The horn arrangement as such wasn't so bad, just in an alternative universe. Not sure whether backing tapes were used (by that time they employed them abundantly), Beard has earphones, but he might be listening to just a click. Of course, if a backing tape was running, that meant they couldn't sit a bar or two out to help the horn section catch up. Everything comes at a price.
This will probably get me bashed, but I think ZZ Top are one of the most overrated bands ever. I find very little trio ingenuity in them, give me Cream, Police, Robin Trower, UK, The Jimi Hendrix Experience, ELP, Rory Gallagher or Rush any day, they have all stretched the format. Much like the Ramones, ZZ Top have this cartoonish image that made them an international brand (mostly via their videos), but the music? There is nothing in it that REQUIRES them to be a trio (certainly not improvisational ambition or going off on tangents), it's just an image thing, like Sabbath or Ozzy operating without a visible keyboarder. I've seen ZZ Top live together with Status Quo. In terms of energy, Quo wiped the floor with them and they didn't use tapes to augment their sound either.
I also have issues with calling a band 'rootsy' that uses tapes as much as they do. If Muse feel they have to do it, ok (not that I like them, but their music is orchestral). With ZZ Top, I always wondered why. Sure, it would sound sparser live and they would have to decide more often what part to play and what to leave out, but that is the charm and the challenge of a trio.