Here you go, I did what I said, and made a script according to your variables, but much more easier to look at; it is just a copy and paste of color randomizing for each body part. I hope this works as the SOLUTION and if you have any problems, reply and tell me what happened. 
EDIT: I made all of the Color3 RGB values, (100, 100, 100), because I wanted you to change them accordingly to your desired part randomizing color, as I stated in the script. I got that color as it was the one from the simple, but WORKING script. This is like your complex script AND the working script, just much more neat. If this is not what you wanted, reply with anything, I would be glad to help, as I am trying to become a full member of the DevForum! 
NOTE: If you want all parts corresponding to eachother, to be the same color, use the same “math.random” variable. You can also delay each body part changing by adding “wait()” commands in between their changes.
-- Made by Araknala for Secretum_Flamma's DevForum post.
-- If you want all parts corresponding to eachother, to be the same color, use the same "math.random" variable.
while wait(0.25) do
local randomTorso = math.random(1, 8)
if randomTorso == 1 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100) -- Change these RGB values, and the ones below, to the desired colors; for each random number chosen.
elseif randomTorso == 2 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
elseif randomTorso == 3 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
elseif randomTorso == 4 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
elseif randomTorso == 5 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
elseif randomTorso == 6 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
elseif randomTorso == 7 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
elseif randomTorso == 8 then
script.Parent["Body Colors"].TorsoColor3 = Color3.fromRGB(100,100,100)
end
local randomHead = math.random(1, 8)
if randomHead == 1 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100) -- Change these RGB values, and the ones below, to the desired colors; for each random number chosen.
elseif randomHead == 2 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
elseif randomHead == 3 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
elseif randomHead == 4 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
elseif randomHead == 5 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
elseif randomHead == 6 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
elseif randomHead == 7 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
elseif randomHead == 8 then
script.Parent["Body Colors"].HeadColor3 = Color3.fromRGB(100,100,100)
end
local randomLeftArm = math.random(1, 8)
if randomLeftArm == 1 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100) -- Change these RGB values, and the ones below, to the desired colors; for each random number chosen.
elseif randomLeftArm == 2 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftArm == 3 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftArm == 4 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftArm == 5 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftArm == 6 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftArm == 7 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftArm == 8 then
script.Parent["Body Colors"].LeftArmColor3 = Color3.fromRGB(100,100,100)
end
local randomRightArm = math.random(1, 8)
if randomRightArm == 1 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100) -- Change these RGB values, and the ones below, to the desired colors; for each random number chosen.
elseif randomRightArm == 2 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
elseif randomRightArm == 3 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
elseif randomRightArm == 4 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
elseif randomRightArm == 5 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
elseif randomRightArm == 6 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
elseif randomRightArm == 7 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
elseif randomRightArm == 8 then
script.Parent["Body Colors"].RightArmColor3 = Color3.fromRGB(100,100,100)
end
local randomLeftLeg = math.random(1, 8)
if randomLeftLeg == 1 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100) -- Change these RGB values, and the ones below, to the desired colors; for each random number chosen.
elseif randomLeftLeg == 2 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftLeg == 3 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftLeg == 4 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftLeg == 5 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftLeg == 6 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftLeg == 7 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
elseif randomLeftLeg == 8 then
script.Parent["Body Colors"].LeftLegColor3 = Color3.fromRGB(100,100,100)
end
local randomRightLeg = math.random(1, 8)
if randomRightLeg == 1 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100) -- Change these RGB values, and the ones below, to the desired colors; for each random number chosen.
elseif randomRightLeg == 2 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
elseif randomRightLeg == 3 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
elseif randomRightLeg == 4 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
elseif randomRightLeg == 5 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
elseif randomRightLeg == 6 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
elseif randomRightLeg == 7 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
elseif randomRightLeg == 8 then
script.Parent["Body Colors"].RightLegColor3 = Color3.fromRGB(100,100,100)
end
end