Key to your conundrum ("I haven't been able to find as coherent a pattern"), is there isn't a coherent pattern. At least not a systematic one. I'll endeavor not to repeat too much of what @Majestic12 has said with his answer.
Like Weapon Speed Factor (pp.68-69, 95 in the 2nd edition Players Handbook), or Weapon Type vs Armor Type Modifiers (p.90, Table 52 in the 2nd edition Players Handbook), the popularity of the Treasure Type tables/matrices can be illustrated with the following formula:
Not Used >> Not Used as Designed >> Used as Designed
So don't feel bad about failing to find meaning in them.
I've quoted below the explanatory page from the original Monster Manual for AD&D (1977, p.5). As a side note, this explanation for how to use the monster Treasure Type tables is paraphrased by Don Turnbull in the AD&D Fiend Folio (1979, p.7), is repeated nearly verbatim again in the Monster Manual II (1983, p.6) and, with the verbiage cleaned up a bit, it can also be found in the 2nd Edition Monstrous Compendium (1989, p.-).
TREASURE TYPE refers to the table which shows the parameters for various types of valuables which the monster in question might possess. If individual treasure is indicated, each individual monster of that type will carry, or possibly carry, the treasure shown. Otherwise, treasures are only found in the lairs of monsters, as explained above. Note also that although an encounter occurs in monster's lair, and the monster possesses some treasure type, this does not automatically mean that the adventurers will gain treasure by defeating the monster. Most treasure types show probabilities for various kinds of wealth to occur in the treasure of the monster. If subsequent dice rolls indicate that the form of treasure is not in the monster's trove, then it is not there, and it is quite possible to come up with no wealth (including magical items) of any sort in a monster's lair despite the fact that a treasure type is indicated. Finally, it must be stated that treasure types are based upon the occurrence of a mean number of monsters as indicated by the number appearing and adjustments detailed in the explanatory material particular to the monster in question. Adjustment downwards should always be made for instances where a few monsters are encountered. Similarly, a manor adjustment upwards might be called for if the actual number of monsters encountered is greatly in excess of the mean. The use of treasure type to determine the treasure guarded by a creature in a dungeon is not generally recommended. Larger treasures of a given type are denoted by a multiplier in parentheses (✕ 10, etc.) — not to be confused with treasure type X.
The bolded sections show Gygax's ubiquitous fondness for dice-induced randomness.†
The italicized section makes room for an important caveat — planned encounters ('creatures found in dungeons' to paraphrase Gygax) are an important general exception to using the Treasure Types table.
Quoting from the Fiend Folio (1979, p.7),
If dice rolls indicate that a particular treasure component is not in the monster's lair, it is simply not there; it is thus quite possible to gain no treasure from defeating a monster in it's lair, despite the fact that a treasure type is indicated.
Treasure types are based on the appearance of a mean number of monsters of that particular type, as indicated by the "number appearing". In instances where fewer, or more, monsters of that type are encountered, the treasure should be reduced, or increased, in value.
These explanations create some problems for the thinking gamer.
First problem, as can be deduced from literally every published adventure and RPG game endorsed by TSR/Wizards of the Coast; there is always treasure to be gained from defeating a given monster in published adventures, table top or online. Why should this ever be different often enough for a home campaign to need the randomness and complexity of a Treasure Table?
Another difficulty is this method produces very swingy results and internally inconsistent results. Take kobolds‡, listed as having Treasure Type: J on each individual, with types O and Q (x5) in lair.
As you can see from the percentages given in the Monster manual appendix Treasure Types table, a kobold lair of 400 individuals has a 1-in-40 chance of having no treasure. A kobold lair of 40 individuals has the same chance, 1-in-40.
But kobolds are guaranteed to be personally carrying 3-24 cp each (treasure type J is 3-24 cp); even though 1-in-4 lairs will have 0 cp in the tribal coffers! What? That makes no sense. Must be 1-in-4 kobold tribes are thoroughly socialist (I kid but I trust you see what I mean).
Worse, in the case of zero lair hoard, even adjusting the lair amount upwards for a tribe well above the mean value, as suggested in the various monster manuals, gives no increase in actual treasure amount (multiply by zero gets you zero every time with real numbers).
Gygax rationalizes it all in "game logic" terms in the AD&D Dungeon Masters Guide (1979, pp.91-93). A few choice quotes;
This is not a contradiction in the rules, but an admonition to the DM not to give away too much!
Assign each treasure, or lack thereof, with reason.
Thoughtless placement of powerful magic items has been the ruination of many a campaign. Not only does this cheapen what should be rare and precious, it gives player characters undeserved advancement and empowers them to become virtual rulers of all they survey. This is in part the fault of the writer, who deeply regrets not taking the time and space in D&D [a.k.a. OD&D] to stress repeatedly the importance of moderation.
AD&D means to set right both extremes [abounding PC wealth and killer dungeons]. Neither the give away game nor the certain death campaign will be lauded here.
In those instances where a randomly discovered monster has a nearby lair, and somehow this lair contains treasure, do not allow the dice to dictate a disaster for your campaign.
Basically the DM is to use the Treasure Type tables by largely not using them.
Beyond what this question asks are a few related outsider opinions about how the game has changed since it's inception. These opinions, while my own, have been gleaned through many long discussions with those who have played for decades and from reading through many old game products. Here goes...
You will find that questions around assigning monster treasure get even more confusing when considering the 2nd edition of the game. While some of the wiggle words are still there in the Monstrous Compendium,
If individual treasure is indicated, each individual may carry it or not at the DM's discretion
there is even more obvious direction to the effect that the DM should take more control over the game than dice rolls typically allow,
Major treasures are... most often designed and placed by the DM.
and a little later,
Do not use the tables to place dungeon treasure, as numbers encountered underground will be much smaller.
That last bit made no sense to me or anyone I talked to who played back in the day. Think about it, some of those monsters only live in dungeons so how could their numbers be "much smaller" than what is given in their description?
In the 2nd edition AD&D Dungeon Masters Guide (1989, pp.80-84), like the AD&D Dungeon Masters Guide (1979), there is considerable space devoted to thinking about treasure in one's campaign. It reads like something written in committee, a nice change of pace (maybe) from Gygax's turgid prose, but confusing in it's own way.
Quoting one little tidbit seen commonly whenever the "best" way to game comes up for discussion.
Now, if both DM and players enjoy a particular type of campaign and are having a good time, there is no problem to fix. However, more often than not, these two extreme adventuring styles lead to game problems.
That's pretty much the whole of the Dungeon Master's Guide, from any edition, summed up in two sentences! Is it not?
Then along comes 3rd edition, and it systematizes most everything about the game including monsters and their treasure. Rules Lawyering has always been a thing but now with 3rd edition the Power Gamer and/or Munchkin come into their own in ways that were not possible in prior editions.
The 4th edition levels the playing field by smoothing the highs and lows found in previous editions. Apparently most people found it stultifying since they left in droves; many going on to play the 3rd edition clone Pathfinder and many more going to other games/hobbies.
The 5th edition seems to have brought many of the old-timers back to the game and roped in many new ones besides. It uses more systematization than the original game but puts the focus squarely on the DM "owning" the campaign and (outside of the Adventurer’s League) tailoring it to suit the needs at the local table. It has some new ideas gained from 40 years of TTRPG playing but captures the feel that set Gygax's (and Arneson's) game apart from all the others back in the day.
In that vein, I'll give Gygax the last word, quoting from Dungeon Masters Guide (1979, p.7),
As the creator and ultimate authority in your respective game, this work is written as one Dungeon Master equal to another. Pronouncements there may be, but they are not from "on high" as respects your game... When you build your campaign you will tailor it to suit your personal tastes. In the heat of play it will slowly evolve into a compound of your personality and those of your better participants, a superior alloy... As the author I also realize there are limits to my creativity and imagination. Others will think of things I didn't, and devise things beyond my capability. As an active Dungeon Master I kept a careful watch for things which would tend to complicate matters without improving them, systems devised seemingly to make the game drag for the players, rules which lessened the fantastic and unexpected in favor of the mundane and ordinary.
So say we all.
† See for instance Appendix A: Random Dungeon Generation in the AD&D Dungeon Masters Guide (pp.169-173), if you thought the Treasure Table was confusing.
‡ Not to be confused with Tucker's Kobolds, free PDF here as of 4-19-2016. http://media.wizards.com/2014/downloads/dnd/TuckersKobolds.pdf