I got home, checked my i.d. books, and found out I was wrong. It looks like the fish in your first photo is actually a southern hake, Urophycis floridana. The fact that there are two separate dorsal fins distinguishes it from the brotulas. Also, I found a couple of pictures of the southern hake that show a series of white spots along the lateral line, just as in your photo, plus one of the i.d. books notes that the southern hake has a "lateral line dark with row of pale spots". Southern hake it is.
They reportedly "grow to 14 in", and "although this is normally an offshore species, southern hake young move into shallow water and saltier bays during the winter months". As your fish doesn't look particularly small, it may be uncommon in a jetty environment in May. On the other hand, the bearded brotula, which is what I originally thought the fish to be, is particularly listed as being found near jetties in the Gulf. So it's still possible that the fish SeaYoda saw before at night is a bearded brotula. When you look at pictures of the two fish, they are pretty similar in appearance. The brotula, however, gets up to 3 ft. in length.
By the way, my favorite i.d. book for fish of the NE Gulf of Mexico is Dr. Bob Shipp's "Guide to Fishes of the Gulf of Mexico". I bought this about 6 years ago, and haven't seen it for sale since, so it may be out of print. The book specializes on fish of the Alabama and FL Panhandle coast.