Take a look at this:
..C........L........U..... clue 3 mod 9
.....F........O........X.. fox 6 mod 9
........I........R........ rain 9 mod 9
.B........K........T...... basket 2 mod 9
....E........N........W... new 5 mod 9
.......H........Q........Z haze/quiz 8 mod 9
A........J........S....... jades 1 mod 9
...D........M........V.... moved 4 mod 9
......G........P........Y. gypsy 7 mod 9
What we have here is
in row N (numbering from 1), all the letters whose alphabet position is (3N rem 10) mod 9, where "rem" means "the remainder on dividing by". The Nth of our allegedly mnemonic words (or in one case word pairs) contains all of those letters and a few more in order to make an actual words (though not as few of them as possible; e.g., we could have had JARS instead of JADES, and RIM instead of RAIN).
I'm quite at a loss, though, as to
why anyone would want a mnemonic for this, still less why one that puts other letters in the words. I suspect I'm missing some other way of looking at what's going on that makes it all much clearer...
Aha, noedne has cracked it in a comment on this answer.
It's a mnemonic for which letters go in which boxes for the "Elian Script" version of the pigpen cipher, as found in this puzzle solved by Deusovi. (To whom the hint was obviously pointing.) So e.g. the letters CLU correspond to the top-left box, hence "J-like" encodings, then the letters FOX to the top-centre box, hence "U-like" encodings, then the letters IR to the top-right box, hence "L-like" encodings, etc.
You might want to go and upvote some of noedne's things :-).