Goldburn is born in the same way as every other kaiju, by absorbing the emotions generated when people feel constrained by the world around them. Why, then, is it friendly when every other kaiju isn't? Because the emotions it grew on were Chise's feelings of being left out and unable to help the rest of the team protect the world.
The Dynazenon team all primarily wear RGB colors note Koyomi wears green, Yomogi wears blue, Yume and Chise wear red, meanwhile their Evil Counterpart the Kaiju Eugenicists features CMYK colors on their arm bands note Mujina is cyan, Onija is magenta, Juuga is yellow, and Sizumu is grey/black . Gauma wears colors which are prominent in both schemes —blue and yellow— which shows his ties to both groups.
Where those colors are placed on his outfit also reflect his relationship with the characters represented by those colors. Juuga was friends with Gauma 3000 years ago, but now Gauma sees him as an enemy despite the latter's continued admiration of him; fittingly, the yellow parts of Gauma's clothes resemble mummy bandages, symbolizing a dead friendship. Yomogi saved Gauma's life, and their friendship happened in the present day; this is reflected by the blue parts of his outfit being normal, everyday clothes, or clothes of the living.
This crosses over with Fridge Horror but Gauma wields Dyna Diver, a submarine that can only really function in water, and episode 10 reveals Gauma died soaked, submerged in a pool of rain water prior to being revived.
The theme continues with Yume and Koyomi. Yume wields Dyna Wing an airplane and the root of her trauma is that her sister died falling off a tall building. Koyomi has Dyna Striker a race car and his trauma is that he ran away as fast as he could from Inamoto’s shady offer.
Each Kaiju Eugenicist and Yomogi has a subtle case of Personality Powers in the kaiju they control:
The kaijus Juuga control have abilities that prevent the enemy from running away, Greyjhom by using its Teleport Spam to quickly close the distance and Gibzorg by immobilizing the enemy. Juuga's main desire is to close the distance between Gauma and himself, which manifests in the kaiju he controls.
Onija's kaijus note Shallbandes, Banadodon and Bullbind all have abilities suited for mass-destruction and frequently involve Stuff Blowing Up, fitting Onija's Ax-Crazy and straightforward nature.
The kaijus Mujina control (or in Garnix's case, attempted to control) all have abilities related to flattening objects; Didoras can turn 3D objects into 2D, Bullbind can crush buildings by amplifying gravity, and the people who disappeared under Garnix's ability only leave their 2D shadows behind. Mujina feels that controlling kaiju is her only purpose life; essentially, she sees herself as a Flat Character.
The kaiju under Sizumu's control all have a second, hidden form; Neophobia has its upside-down mode, whilst Gagula can go One-Winged Angel by fusing with the other Eugenicists. This reflects Sizumu's duplicitous, secretive nature, as well as representing that he has a kaiju hidden within himself.
The kaiju Yomogi performed Instance Domination on all have a rainbow motif; Zaiohn can paint its surroundings with random colors, and the second form of Gagula has rainbow-colored parts on its body. Unlike the Kaiju Eugenicists, who believe bonds with others obstruct a person's freedom, Yomogi values those very bonds; metaphorically speaking, the Eugenicists want to separate colors, whilst Yomogi wants to mix them.
The part of Dynazenon that Yomogi pilots is roughly humanoid, with functional arms, legs and a head, and in a live action work would have been portrayed by someone in a costume... just like one of the kaiju. So Yomogi is basically in charge of controlling the most kaiju-like independent piece of Dynazenon. Fitting for someone capable of Instance Domination.
The one who practiced as a backup pilot of Dynasoldier is Chise. While she is not capable of Instance Domination, she still becomes capable of ‘controlling’ a kaijuu by hatching, naming and befriending Goldburn.
Finally, Gauma, the one on the team with most experience in controlling Kaiju as a former Eugenicist, has overall control of Dynazenon, befitting his greater experience with Kaiju.
In episode 2, Yomogi was struggling to do anything with Dyna Soldier besides moving its arms. Why was he able to jump to combine with Dyna Wing all of a sudden?
I assumed it was because Yume was doing all the work since Dyna Wing just needs to attach to Dyna Soldier back and she could carry him around.
