Ggtkuk

“Well, that's all great but how do you remember it?” George asked.

“Easy,” I replied pointing at a nearby board. “Just remember these words: Clue, Fox, Rain, Basket, New, Haze and Quiz, Jades, Moved, and Gypsy.”

“It’s good you're using the Oxford comma. That does help. Thanks."

What were they talking about?

Hint:

“And you say that a devious, devious person knows all about this, eh?” confirmed George. I smiled. “Yes. They recently introduced me to it.”

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 :-).

The words

form a pangram,

so perhaps they are talking about

the English alphabet.

Partial idea

The Oxford comma is used to separate the list items Moving, and Gypsy.

But there is no comma in Haze and Quiz which suggests that they belong as a pair.

There is already an and in the sentence, so it is not needed for the pangram suggested.

Building again on Gareth McCaughn, could it be

A cypher, such as the one where you wrap a strip of paper round a something-o-hedric cylinder. So the mnemonic would be for mentally decoding the cypher.

Most of it has been presented by Gareth McCaughan, but I want to add that maybe he wants to remember the

alphabet?

Evidence:

Perhaps this would be better:

A........J........S....... jades     1 mod 9

.B........K........T...... basket    2 mod 9

..C........L........U..... clue      3 mod 9

...D........M........V.... moved     4 mod 9

....E........N........W... new       5 mod 9

.....F........O........X.. fox       6 mod 9

......G........P........Y. gypsy     7 mod 9

.......H........Q........Z haze/quiz 8 mod 9

........I........R........ rain      9 mod 9

Hint:

devious devious: 1st devious: anagram indicator; 2nd: base; result = @Desouvi