So far puppeteers were political organizations where members have to follow rules but what is source to their commands and rules comes from above where emotional, rational and impulsive urges trickle their effects down to organizations. Ruling impulses of the powerful is close to ruling their decisions and priorities. Some are born powerful but they are also exposed to various temptations and through influencing public awareness of various urges even the most powerful groups could be influenced as long urges feel appealing and worthy of their time.
Annunaki level can symbolize god complex ruling those below but in this case "god" is manic looking low brow creature dressed in primitive clothing. Some in power have called themselves gods like many royalties and princely offsprings did for thousands of years. Like many deities they are moody praise demanding megalomaniacs that are willing to cause deaths to almost all if few rebel. That deity level is ruled by reptilian level with likely reptilian brain. Low brow deity is like reptile who doesn't negotiate while self absorbingly chasing its self-gratifying goals, doesn't negotiate and just tries to get what it wants without caring for suffering of others. Only care they occasionally show is usually towards their offspring. Efficient productivity is not something that level could easily (if at all) plan. Increasing amount of possessions comes through violence. Emotions control behavior and if god level fails at getting what it wants then "higher" reptilian behavior with its angry hissing and selfish attitude takes over as facade of refined civility/nobleness falls away and gets replaced by subhumanly simplistic emotionality. This reptilian state could be extra likely on those kings and other rulers who were alcoholics or cocaine/amphetamine users and couldn't think much but wanted much and felt mostly too strong or careless.
Gray level is more alien level which controls primitive reptilian puppeteers and many people spend their entire lives without ever learning to control those primitive behaviors which may be reason why that level of control is shown as alien. As far as i've learned to control the tricks that worked at controlling self felt very counter-intuitive (for example imagining droplets condensing on imaginary walls around self having calming effect and hundreds other similarly weird tricks for controlling other things). Emotionless (unlike lower level ones) and genderless appearance suits this level well. It can involve cold calculating planning which knowingly uses reptilian savagery and megalomania for its goals including provocations to get less rational and overtly violent responses when outcome seems self serving. This level may also involve regulating self if by allowing lower level behavior through if it seems necessary.
On more primitive levels i've used understanding of my limitations in writing knowing about how much i can read in day before ability to process information in this day runs out, how much can i read, which entertainment or music helps with working and which overstimulates (like ~100% of tv programming) to point that reality becomes unbearably dull.
On weirder level i also planned many things knowing that my brain forgets particular things in certain time and even more so if i think them while high on cannabis but at same time i knew that it would help for reaching goal,which i temporarily forget for up to months. As side effect of this planning i've frequently reached point where i feel i've figured out something i wanted to know in some stoned pipedream. Of course it took time to learn what weird memory and willpower tricks cannabis causes but after smoking it for thousands of times experience fragments accumulated enough for practical skills. Often i used this forgetful stoned path for reading about things that were too boring for sober study or too scary/distractingly stressful.
Different very common reason i used this dividing reading was consideration to limits and abilities of memory. On one side memories are fleeting but on other side larger amount of ideas are easier to remember at least for me when i decide to deal with them on particular near future day or easy to remember date. Then i likely forget it but when i notice calender is showing time i decided to do something then i usually remember plans for that day.
As much of brain activity follows 24 hour rhythm with stress hormones and energy levels fluctuating almost like clockwork it takes some insight to know how to stay on good path so most powerful example of something on that level would be some really advanced artificial intelligence that isn't hindered by its own emotions but knows well how much time passed from some point, how long some mental state in humans lasts and how much they could keep doing something (from mental activity to load carrying), how long can their mental state be useful before exhaustion, which are visible, including infrared, or electric or chemical signs of various mental and physical states before/after energy reserves run out, which background environment would help with optimal functioning.
Galactus level. Galactus is character from comics who survived through death of old universe and birth of new universe with power to consume planets for its own benefit and who looks like life forms who discover it so when humans met it then it resembled human as shown above. It can represent will and ability to travel between planets and consume those even if it means killing all life on these planets. Such behavior is likely among any interstellar civilization that travels around seeking planets to take over and consume to restock on materials. If every birth of universe creates advanced life who can travel then in way this behavior can't be killed by temporary end of universe as new stars and habitable planets can keep on recreating pretty much same empires.
Being advanced enough interstellar force would probably involve manufacturing proxy fleets which could be organic or entirely machine civilizations as apparently unrelated alien forces who don't share guilt over what one of them does.
Movies and many sci-fi works have for at least decades involved people in thinking how to serve such force by for example repeating theme that planet dies for using enough resources so new ones need to be reached and colonized. These works don't insist viewer has to serve this goal but it heavily insinuates that those expensive and technically advanced works have to be made into reality go extinct from inaction. Economically there is way more money and power to be gained from running a interplanetary empire compared to what can be gained from religions where deity needs donations and human intermediaries.
Any emotional or coldly rational brain power can serve this larger will to survive and expand in universe.
Before 2014 i had ignored Cthulhu as some random fiction but during 2014 i managed to map many weird part of mental maps and shapes that control or mediate impulses and desires seemed quite similar to Cthulhu with wings in back and tentacle type things in front (and back). That shaped structure with its wings and tentacles controls impulses and all lower level puppeteers on first illustration are basically following impulses. Another Lovecraftian creature that i found as controller of impulses was shaped like "mi-go" as sort of winged creature pushing onwards and giving warmth when imagined as red). These creepy shapes are not always entirely visible but only with small parts at time.
At least to me a thought of tentacle hanging from above into object can cause mindless drive to get close to that object or obsess over it. If tentacle reaches from below then in seconds it creates angry urge to also get closer to that object or just get angry at that thing.
What Lovecraft wrote about Cthulhu is not very different from Galactus. Both travel around universe as sort of undying or temporarily dying force that takes areas over while in general being maddening and unstoppable.
For example: "They were not composed altogether of flesh and blood. They had shape [...] but that shape was not made of matter. When the stars were right, They could plunge from world to world through the sky; but when the stars were wrong, They could not live. But although They no longer lived, They would never really die. They all lay in stone houses in Their great city of R'lyeh, preserved by the spells of mighty Cthulhu for a glorious resurrection when the stars and the earth might once more be ready for Them". " Another race–a land race of beings shaped like octopi and probably corresponding to the fabulous pre-human spawn of Cthulhu–soon began filtering down from cosmic infinity and precipitated a monstrous war which for a time drove the Old Ones wholly back to the sea".
Something not made of matter can represent metaphorical body. Also they depend on stars being "right". For any interstellar colonizer stars would need to be in good enough state to at least not blow them up in supernova or gamma ray bursts. When they stop living from lack of energy then they could preserve their memories in some resilient data storage format that could be read by other civilizations that get influenced by these memories.