Simple script to print a ScreenGui in a player's PlayerGui on connect not working, why?

I'm doing a test script to play around with for loops & looping through available players. The script is simple!

print("Script initiated.")
function Run()
    for i, v in ipairs(game.Players:GetPlayers()) do -- Get available players!
        wait(12); -- In case contents inside PlayerGui has not been loaded!
        print(v); -- Prints the current iteration, player's name (current iteration).
        print(game.Players[v.Name].PlayerGui.testFind); -- Simple, there's a ScreenGui!
    end
end

game.Players.PlayerAdded:connect(Run)

Very simple. Yet doesn't work. Why!?

It works in studio and this is what it outputs:

Script initiated.
Player1
testFind

However if you try it online, there's suddenly an error!

Script initiated.
Player... added
Arithmeticity
testFind is not a valid member of PlayerGui

The script is placed in ServerScriptStorage.

Here's the model if you want to take a look at it and see why: click to see the model.

Am I missing something? Please help me as this is confusing me. It should be e-z-p-z.

Update(s):

Just got helped by ScriptGuider. He says that server cannot access the contents of PlayerGui so that may be a possibility. I'm now trying to work around it instead of doing this method. See how it goes and all, so far so good. Thanks to ScriptGuider! If ScriptGuider reads this, maybe post a reply so I can accept your answer perhaps.

Edited the script yet again to include WaitForChild. Here it is:

print("Script initiated.")
function Run()
    for i, v in ipairs(game.Players:GetPlayers()) do 
        print(v);
        game.Players[v.Name].PlayerGui:WaitForChild("testFind");
        print(game.Players[v.Name].PlayerGui.testFind);
    end
end

game.Players.PlayerAdded:connect(Run)

Output has been changed, it's now this:

Script initiated.
Arithmeticity.
Player ... added
Infinite yield possible on 'Players.Arithmeticity.PlayerGui:WaitForChild("testFind")'
Stack Begin
Script 'ServerScriptService.testIterations', Line 5
Stack End

I have also updated the model so if anyone can please take it and take a look in their own game, that'll be really helpful!

Past edit 2/1/2017:

print("Script initiated.")
function Run()
    for i, v in ipairs(game.Players:GetPlayers()) do 
        print(v);
        repeat wait() until game.Players[v.Name].PlayerGui.testFind;
        print(game.Players[v.Name].PlayerGui.testFind);
    end
end

game.Players.PlayerAdded:connect(Run)

The output is pretty much the same results. Why is this happening!?