How do I make it so that a certain part of a script only starts when touching a certain part?

I'm making a game with a script THAT CHANGES THE PLAYERS SCORE EVERY SECOND, AND RESETS BACK TO ZERO WHEN THE PLAYER DIES. This works fine. However, I need the timer to only start when the player isn't touching a certain part (Called "StartPart"). I still need to keep the same aspects of the script I meantioned above (In CAPITALS). Sorry if the script is a bit confusing. Here's the script I have currently:

local Players = game:GetService("Players")
    local UpdatePoints = false

    Players.PlayerAdded:Connect(function(Player)   
            Player.CharacterAdded:Connect(function(Character)
                    UpdatePoints = true

                    local Leaderstats = Instance.new("Folder")
                    Leaderstats.Name = "leaderstats"
                    Leaderstats.Parent = Player

                    local Points = Instance.new("IntValue")
                    Points.Name = "Points"
                    Points.Parent = Leaderstats

                    Player.leaderstats.Points.Value = 0

                    local Humanoid = Character.Humanoid
                Humanoid.Died:Connect(function()
                            UpdatePoints = false
                            Player.leaderstats.Points.Value = 0
                    end)

                    while (UpdatePoints) do
                            wait(1)
                        Player.leaderstats.Points.Value += 1
                            if not (UpdatePoints) then
                                    break
                            end
                        end
                end)
end)