How do I make a SpotLight turn on when a brick is a certain color?

You have to put BrickColor.new("Colorname"). Also 'if' statement conditions have to have a == sign, which means it is equivalent to, one equals sign means to appoint something.

    if Game.Workspace.CartRegen.Cart.On.BrickColor == BrickColor.new("Bright red") then

local Object = Game.Workspace.CartRegen.Cart.On
function updateLight(Object)
    Object.SpotLight.Enabled = Object.BrickColor == BrickColor.new("Bright red") and false or true --If Object is red, then disable the light. Otherwise, enable it.
end
while wait(0) do
    updateLight(Object)
end

These comments above would certainly answer your problem, however relying on infinite loops to solve your problems can cause lag in the future. To avoid such loops, we require events to fire whenever a specific thing happens. In this case, we want to see when that brick changes colour and to then turn on or off the light. If you look on the wiki, however, you will find that there is no .ColorChanged() event. But, there is a .Changed() event. This is how to use it:

local part = Game.Workspace.CartRegen.Cart.On

part.Changed:connect(function(property) --The argument passed to the event is the name of the property that changed.
    if property == "BrickColor" then        --Make sure the property changed is the colour.
        if part.BrickColor.Name == "Bright red" then        --The name property or BrickColors makes this check easier.
            part.SpotLight.Enabled = false
        elseif part.BrickColor.Name == "Bright green" then  --You could probably just replace this line with 'else' but I don't know if you intend on changing the part to colours besides red and green.
            part.SpotLight.Enabled = true
        end
    end
end)

while true do
    if Game.Workspace.CartRegen.Cart.On.BrickColor == "Bright red" then
        Game.Workspace.CartRegen.Cart.On.SpotLight.Enabled = false
    elseif Game.Workspace.CartRegen.Cart.On.BrickColor == "Bright green" then
        Game.Workspace.CartRegen.Cart.On.SpotLight.Enabled = true
    end
end

With given information, all you need to do is that. Should work, at least.

The problem with this script is that the if,BrickColor, and while statement is Wrong

Here is the fixed script

while true do
    if Game.Workspace.CartRegen.Cart.On.BrickColor = BrickColor.new("Bright red") then
        Game.Workspace.CartRegen.Cart.On.SpotLight.Enabled = false
    else if Game.Workspace.CartRegen.Cart.On.BrickColor = BrickColor.new("Bright green") then
        Game.Workspace.CartRegen.Cart.On.SpotLight.Enabled = true
    end
wait(How long time it have to wait)
end

When you use the if statement, then it uses the comparison operator which is this ==. When you want to Compare or assign a BrickColor, then you need to use BrickColor.new("Colorname for example Bright red") just replace the Colorname with this. All while statement must have a wait() function (which makes it wait until it exceeds the end then it continues) or the game will crash because your computer will use so much CPU that you'll not be able to play it.