The current approach to “authentic color” in retro gaming consists of researching which standards were in common usage, and the characteristics of TVs commonly in use.
The problem is, pixel artists probably never actually adhered perfectly to any set of standards.
This is Takashi Tezuka, the sprite designer for Super Mario Bros 3. Check out the colors on that small monitor.
That is a decidedly warm color temperature. It’s not 9300k at all. It’s 6500k, 100%. What else have we gotten wrong?
Probably the best we can do to determine which colors are “correct” is to find a photo like the one above.
Another bit of evidence: SMB sky should be purple as confirmed by direct quotes. It’s purple with a warm temp, blue with a cool temp on almost any TV decoder.