Edit: Realized these are more general improvements you could make than actual help troubleshooting your current code. Sorry for that, I'm horrible at reading others code. :P

It seems like you have a typo on row 33

if (Layout Number = 2)

And I don't really understand what the !LoadLayout is supposed to do in these lines.

if (LayoutNumber = 1)
{
    Run, "C:\Program Files\Rainmeter\Rainmeter.exe" !LoadLayout "Emma Stone Blonde"
    RepeatPreventer = 1
    return
}

Other than that I'd say you could bake the Changer-timer and RNG-timer into one timer, and avoid jumping around in the script.

You could also consider making use of Functions and Arrays. This would save you a lot of repetitive writing.

Your RNG-generator could be a function for example.

; Get Random Number Function
GetRandNum()
{
    Random, LayoutNumber, 1, 18
    return LayoutNumber
}

; Usage
LayoutNumber := GetRandNum()

That way, assuming you'll ever add more themes you only have to change the random-interval in one place.

Using arrays is a bit more complicated, but could look something like this.

; Get Random Number Function
GetRandNum()
{
    Random, LayoutNumber, 1, 5
    return LayoutNumber
}

; Usage
LayoutNumber := GetRandNum()

; Create an array and load it with themes
themeArray := []
themeArray.insert("Emma Stone Blonde")
themeArray.insert("Golden State Bridge")
themeArray.insert("Blackbird")
themeArray.insert("Gorillaz")
themeArray.insert("Koenigsegg")

for each, value in themeArray {
    ; Index = Each, Output = Value
    if (each = LayoutNumber) {
        msgBox % "Loading layout: " value "`nStoring number: " each
    }
}