RemoteEvents: Why is this happening?

I'm trying to learn remote events etc and I thought the best way to go about that would be to try create random things and manipulate them with remote events. I think I've made a-lot of progress so far but I've run into an issue. Essentially I'm trying to create a selection box around any part that the player is currently hovering over with their mouse, it works for the most part.

GIF of the issue https://gyazo.com/6ac440a161ab9a233b13e759903c8727

LOCALSCRIPT

play = game.Players.LocalPlayer
mouse = play:GetMouse()

if mouse.Target ~= nil then
	while wait() do
		game.ReplicatedStorage.Target:FireServer(mouse.Target)
		wait()
	end
end

SERVERSCRIPT

game.ReplicatedStorage.Target.OnServerEvent:Connect(function(player, target)
	if target == nil then return end
	if not target:FindFirstChild("TargetPart") and target.Name ~= "TargetPart" and target.Name ~= "Baseplate" then
		local part = game.ReplicatedStorage.TargetPart:Clone()
		part.Parent = target
		part.Size = target.Size + Vector3.new(0.2,0.2,0.2)
		part.Anchored = true
		part.CFrame = target.CFrame
		print(target.Name)
	end
end)

The below script is to delete the part whenever the player removes their mouse from the part, I'm pretty sure this is where the problem is occurring, chances are that I just overlooked something really simple.

SERVERSCRIPT For destroying Part, Parented to the Part.

game.ReplicatedStorage.Target.OnServerEvent:Connect(function(player, target)
	wait(target == nil)
	script.Parent:Destroy()
end)

EDIT: So thanks to your guys help I've fixed the issue and improved it greatly, what took up 3 scripts before now only covers 14 lines.

play = game.Players.LocalPlayer
mouse = play:GetMouse()
local selectionbox = Instance.new("SelectionBox")

selectionbox.Parent = play.PlayerGui

mouse.Move:connect(function()
	if mouse.Target == nil then end
	if mouse.Target ~= nil then
    	if mouse.Target.Name == "Baseplate" then end
    	selectionbox.Adornee = mouse.Target
    	wait()
	end
end)

If you're curious of what I was using it for then here's a GIF

https://gyazo.com/68233bf7775ccbf17425345bf7a8d35a

Part 1: How I would do it (skip this if you want the answer to your question) Hey, so instead of creating a new part for the selection box, let's use an instance called SelectionBox.

Let's start by creating this instance and placing it inside StarterGui.

Now that you've created the instance you might be wondering how I can connect it to a part, to do that you just have to set it's Adnornee to the part.

Using your client script we can do this.

play = game.Players.LocalPlayer
mouse = play:GetMouse()
local selectionbox = play.PlayerGui:WaitForChild("SelectionBox") --also gatta wait for things to load :p

if mouse.Target ~= nil then
    while wait() do
	if target.Name ~= "Baseplate" then
		selectionbox.Adornee=mouse.Target
	end
        wait()
    end
end

Part 2: Answer to your question

For the LocalScript we need to remove the check for mouse.Target BEFORE the actual loop starts. Once the loop starts we can check to see if mouse.Target is nil and the target's name is not "TargetPart".

play = game.Players.LocalPlayer
mouse = play:GetMouse()

while wait() do
	if mouse.Target and mouse.Target.Name~="TargetPart" then
		game.ReplicatedStorage.Target:FireServer(mouse.Target)
	end
    wait()
end

Let's destroy the -

SERVERSCRIPT For destroying Part, Parented to the Part. We only need to deal with the main server script now.

In the ServerScript we begin by setting curPart as a global variable.

.Next we can set curPart to be a clone of TargetPart and set that up and if target is nill or doesnt pass our first if statement, we can Destroy() curPart if it exists to remove it once you move your mouse off the part.

local curPart
game.ReplicatedStorage.Target.OnServerEvent:Connect(function(player, target)
    if target == nil then return end
    if not target:FindFirstChild("TargetPart") and target.Name ~= "TargetPart" and target.Name ~= "Baseplate" then
        curPart = game.ReplicatedStorage.TargetPart:Clone()
        curPart.Size = target.Size + Vector3.new(0.2,0.2,0.2)
        curPart.Anchored = true
        curPart.CFrame = target.CFrame
		curPart.Parent = target
        print(target.Name)
	elseif curPart then
		curPart:Destroy()
    end
end)

Please ask questions if you have any.