How do you make it so when the user's mouse is idle, it does something when it is...?

You could connect and disconnect the idle event while the mouse is inside the text label but this may not be the best solution, but a solution nevertheless.

Example:-

local mouse = game.Players.LocalPlayer:GetMouse()
local con = nil

local textLabel = player.PlayerGui.ScreenGui.TextLabel

local function idle()
    print('idle')
end

textLabel.MouseEnter:Connect(function()
    con = mouse.Idle:Connect(idle) -- connect the idle event
end)

textLabel.MouseLeave:Connect(function()
    con:Disconnect() -- disconnects the idle event
end)

I hope this helps, please comment if you do not understand how / why this code works.