OK. It breaks down like this:
Engineering, Operations, Services, and Security: Red
Sciences, Life Sciences, Medical, and Nursing Corps: Blue
Command: Green
It follows the tubes used in color televisions: RGB
https://en.m.wikipedia.org/wiki/RGB_color_model
The color scheme for Command uniforms on TOS was intended to be green. If you're doing the math only 1/4 of the Command uniform suite was (and accidentally at that; yellow and even then it has a slight green twinge...yes even the velour just not as noticeably as with the season 3 double knit).
To wit:
The Command Dress Uniforms - Green.
The Command Coveralls - Green.
The Command Wraparound Tunics - Green
The Command (2268 DN) Standard Duty Tunic - Green
Only one Command uniform piece can be truly considered Gold and that's the (2265-2268 Velour) uniform tunic and even then Bill was leaning toward something with some green in it.
Now having served in uniform myself and now in my current career I have had opportunity to study both real world uniforms and the uniforms in the fictional world of Star Trek and though a fan first, I am a reasercher and nit-picky control freak and in the light of new research even I have had to drop many of my old fan notions of how things were and are. "Fannon" must always give way to fact and intent. And the facts are these: the colors for the the major divisions depicted in the regular Original Series were,
Red for Eng
Blue for Sci
Green for Com
And that's it. Anything else is not only wrong, but would be making up a story only to fit the facts.
John
p.s. Now, who's up for a rousing discussion about the use of the arrowhead for all Starfleet Ships of the Line?