How do I store the gui somewhere else for later use?

Here is your script hopefully fixed, use a serverscript under dummy

local Click = game.Workspace.Dummy.ClickDetector 

Click.MouseClick:Connect(function(player)
    player.PlayerGui.ScreenGui.Enabled = true
end)

If that does not work try this but put your ClickDetector in the Dummy's torso.

local Click = game.Workspace.Dummy.Torso.ClickDetector 

Click.MouseClick:Connect(function(player)
    player.PlayerGui.ScreenGui.Enabled = true
end)

The script just get the player who clicked in the event and get there GUI and make it visible.

So on your line local Click = game.Workspace.Dummy.ClickDetector Player = game.Players.LocalPlayer

You shouldn't get the LocalPlayer over a ServerScript. The LocalPlayer is only used for LocalScripts. The MouseClick event already gives you the player so you would not need it.

I think a ClickDetector only works under a part, so if that does not work use the other codeblock.

You can ask me clarification anytime :)

ScreenGuis all have a property called Enabled. You can use this to say wether a ScreenGui will be visible or not.

local Click = game.Workspace.Dummy.ClickDetector Player = game.Players.LocalPlayer

Click.MouseClick:Connect(function()
    Player.PlayerGui["SCREENGUINAME"].Enabled = true
end)