First of all, I'd like to just throw this out...
Gigan Doesn't have red eyes, he has a red cybernetic visor, and this two plausible reasons... It is likely to portray his half mechanical nature as glowing eyes has often been used to indicate robots made up to resemble living organisms, to show that they are in fact, machines... The other reason dates back to the original Gigan, which was green and gold, not black, and I'm pretty sure i have seen a version that had black eyes... The red glowing visor originates from this version, which fired a beam from it's eyes (or between them) that would neutralize Godzilla's atomic breath. They never showed him fire it in the old movies, but it was shown and explained in the game Godzilla: Monster of Monsters, and after reading it in the manual and playing the game it matched the fact that in most fights with Gigan, Godzilla took the longest time and worst beatings, before he finally used his breath attack. According to that game, it was because he just couldn't do it, because Gigan's gaze was preventing it. As I said, they never showed Gigan fire this beam in the old movies, but rather, it seemed to be a constant effect, represented by a red light shining from between his eyes.
With that said, I would like to just say that I would not like to see the Muto Turned into Gigan, I like the Muto is a it's own and completely new creature, rather than just a revision of a old one. Both the old Ghidorah and Gigan were shown in the old series to be weapons that war mongering aliens would either use, or sell to others to use.
In Ghidorah the Three Headed Monster, Ghidorah was said to have wiped out the civilization of Venus or Mars, which was at least centuries ahead of our current civilization, and then he came to earth to do the same here. When he failed, it was revealed in the sequel movie, Godzilla VS Monster Zero, it was revealed that he was under the control of the people of Planet X (No not the Xilians, despite what the wikis may claim, the People of Planet X and the Xilians are entirely different in biology, culture, and technology) thae fact Ghidorah had turned out to be under the control of an alien race the whole time suggests that Ghidora destroyed mars/Venus under the commands of the people of Planet X. Given the advancement of Mars/Venus, it is highly likely that the planet's people were a space faring race and must have entered into a war with Planet X, a war they lost when Planet X unleashed Ghidorah on them... Later, Ghidorah returned in Destroy All Monsters as a weapon of the people of Kilak, which must have bought him from Planet X, he then returned again with Gigan's first appearance, in which they are both under the control of super evolved alien cockroaches, which controlled them via special audio tapes. That's the last Ghidorah would be seen in that series for a long time, but Gigan returned in Godzilla VS Megalon. In that movie, Megalon, a creature very similar to Gigan, appearing to be cybernetic, having limbs that could combine to become a mechanical drill, spit bombs, and a thunder cannon on it's head, was under the control of the Seatopians, an ancient civilization of people who lived in the hollow earth. When they discovered that Godzilla was coming to fight Megalon, they grew afraid and asked Easter island for help and they responded by sending Gigan to fight for them. Easter Island has long been thought to be an Alien landing site, so it's likely that Seatopia some how had an alliance with some aliens who happens to possess Gigan at the time.
I feel that the space weapon background should remain and it would be more plausible if Ghidorah, since he has already been identified to be an Alien from outer space in King of the Monsters, also turns out to be a weaponized space monster, sent to Earth long ago to conquer it and his destruction by Godzilla set off a signal to the aliens and when they finally answer the signal, they bring Gigan with them.
