What hex colors are produced by dyeing signs?

Question

Story
There are two ways to colour signs in Minecraft: Java Edition:

Colour the sign by holding a dye in your hand, then right-click on the sign.

Use cheats to modify a sign's raw JSON text to something like:
{"text":"Green means go!","color":"green"}

Problem
It seems like the dye colours don't seem to match any of the values used by raw JSON text or formatting codes. Examine the images below:

It doesn't seem like any of the dyes match up to an actual JSON text colour, instead, they all seem to be colours of their own. I would like to match them up to actual hexadecimal numbers so I can have them for a reference. Surprisingly, the Minecraft Wiki does not state the actual colour values.
Core question
What are the exact hex code colours produced by dyeing a sign? (yes, it's dyeing, not dying)

P.S: It seems like the JSON colour dark_gray and Light Gray Dye may produce the same colour.

Mark Giraffe · Answer

If you can't access the code whatsoever for hex codes of each color, then try using an editing software, then try to get the colors of each sign via screenshots.
My results:

Red: (#650000), (101, 0, 0)
Orange: (#65290C), (101, 41, 12)
Yellow Dye: (#656500), (101, 101, 0)
Lime Dye: (#4B6500), (75, 101, 0)
Green Dye: (#006500), (0, 101, 0)
Light Blue Dye: (#3C4B51), (60, 75, 81)
Cyan Dye: (#006565), (0, 101, 101)
Blue Dye: (#000065), (0, 0, 101)
Pink Dye: (#652A47), (101, 42, 71)
Purple Dye: (#3F0C5F), (63, 12, 95)
Magenta Dye: (#650065), (101, 0, 101)
White Dye: (#656565), (101, 101, 101)
Light Gray Dye: (#535353), (83, 83, 83)
Gray Dye: (#323232), (50, 50, 50)
Black Dye: (#000000), (0, 0, 0)

Done with MS Paint.

Bonus! Here are the JSON results from your signs according to the Minecraft Wiki:

Red: (#FF5555), (255, 85, 85)
Dark Red: (#AA0000), (170, 0, 0)
Gold: (#FFAA00), (255, 170, 0)
Yellow: (#FFFF55), (255, 255, 85)
Dark Green: (#00AA00), (0, 170, 0)
Green: (#55FF55), (85, 255, 85)
Dark Blue: (#0000AA), (0, 0, 170)
Blue: (#5555FF), (85, 85, 255)
Aqua: (#55FFFF), (85, 255, 255)
Dark Purple: (#AA00AA), (170, 0, 170)
Light Purple: (#FF55FF), (255, 85, 255)
White: (#FFFFFF), (255, 255, 255)
Gray: (#AAAAAA), (170, 170, 170)
Dark Gray: (#555555), (85, 85, 85)
Black: (#000000), (0, 0, 0)

What hex colors are produced by dyeing signs?

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Problem

Core question

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