I dunno. I think I first read about them in Bjo Trimble's "Star Trek Concordance" and I related to her brief, yet tantalizing, description, based on DC Fontana's script notes from "Journey to Babel" (TOS). I guess I related to the mention of blue skin, antennae, a calm exterior hiding their warrior traits, and Shran having a slight lisp?
I didn't get into organised Star Trek fandom until seeing "Star Trek: The Motion Picture" in December 1979 and, after seeing the film about three times, I made it my mission to find the two Andorian crewmen featured in publicity stills, and (when they finally invented video freeze frame for VCRs) the three Andorian extras playing ambassadorial staff in the San Francisco scenes.
The quest to see an Andorian in an actual episode of TOS was my next passionate mission. Star Trek wasn't screening on Aussie television at that time, but we did have a guy who ran Star Trek Marathons throughout the 80s, at ANZAC House - five monthly episodes on the big screen! It was there that I eventually saw "Gamesters of Triskelion" and "Whom Gods Destroy". The second marathon I attended was a costumed affair, so there was only one choice by that point (see my icon pic, which was my 1980 dress rehearsal shot before the big day):
I started reading all the Blish novelizations, and when I bought my "Mr. Spock's Time Trek" View-master reels, that was the day I realized I'd already seen "Yesteryear" (yay Thelin!), and the brief cameos of Andorians in "The Time Trap" (Filmation's Star Trek Animated series, aka TAS).
I put the screws on the marathon guy to screen "Journey to Babel", but he apologised that the only print he owned was badly damaged: green scratch lines down the middle of most footage, and huge bits missing from many scenes. (Every time Amanda went to speak the scene changed!) However he did run the twenty minutes,or so, that he did have, during the lunchbreak of one marathon - I'm sure that's the origin of the misremembered Bjo Trimble anecdote (about censorship of Star Trek Down Under) in the TOS DVDs bonus features. One of my first conversations with Bjo, when I met her in 1984, was telling her that I'd only just been able to see a badly-chopped 20-minute version of "Journey to Babel" back home!
(I also once joked I'd play a new Andorian at a ST convention: a "Bob Johnston print Andorian": complete with green stripes down the face!)
When news was breaking on the ST II film project, I decided that my perfect Andorian villain (or hero) for a ST movie would be... John Phillip Law (Pygar of "Barbarella"), but alas, Andorians weren't even glimpsed again until ST IV. And then all but ignored in "Star Trek: The Next Generation" (TNG). "Deep Space Nine" (DS9) and "Voyager" (VOY) offered only a few stray references in dialogue.
You can imagine how pleased I was when "Enterprise" (ENT) announced "The Andorian Incident", which was to feature Jeffrey Combs, in what became a frequently recurring Andorian role. With moving antennae to boot!