Unfortunately, I don't have experience studying specimens of Apiocera...but after reading the first few pages of the introduction in Cazier(1), I got the clue that this post (and the mating pair here) are likely A. mexicana. Among other things, Cazier(1) mentions that A. mexicana:

1) Is the only species occurring in Veracruz and Tamaulipas (the contiguous Mexican coastal states just south of Texas), and its range "extends northward through the state of Tamaulipas into Texas and along the coast to Matagorda, Matagorda County, Texas"(1);
2) It occurs along the seashore(1);
3) "So far as known...is widely allopatric from other described species"(1).

The above alone seemed to make a pretty good case for A. mexicana here. And when I went through the description on pg 367 of Cazier(1), it seemed consistent to me with what's visible in both this post and that of the mating pair from nearby Mustang Island, TX. In particular, the abdominal pattern in both posts agrees well with Fig. 115 on pg 460 of Cazier(1) and with (the undissected portion of) this image of the male type image from AMNH.

I also checked the possibility of A. infinita that Andy mentioned. Its male abdominal pattern is shown in Fig. 116 on pg 460 of Cazier(1) (conveniently adjacent to that of A. mexicana!) and its AMNH male type image is here. It doesn't seem to match as well as A. mexicana, and its range, as given in Cazier (mainly along the Colorado River between CA and AZ), is quite disjunct from the barrier islands near Corpus Christi, TX.

So I'd say this is A. mexicana, and will move it to that guide page if there is consensus from others.

I was just noticing and fixing that... I had taken care of that glitch once before, but evidently it shows up again whenever I edit my profile.

That is, whenever I go to make a new post, the "County" field is automatically pre-filled with my name.

What I would prefer to happen to me is the other thing that happened to you here...running into apiocerids :-)