How to open GUI when clicking a part?

PlayerGui

When a player joins the game, all of the contents inside StarterGui are locally cloned into that player's PlayerGui, so if you want to mess around with the guis of a specific player, it would be best to run your code on a localscript, as MouseClick replicates and the first parameter of MouseClick is the player who clicked.

So, you can match the player who clicked with the localPlayer to see if the localplayer is the one who clicked the button.

--Localscript (Preferably inside VehicleSelctionGUI.Frame)
local Part = --Whatever part you are using
local Player = game.Players.LocalPlayer

Part.ClickDetector.MouseClick:Connect(function(plr)
    if plr == Player then
        script.Parent.Visible = true --if this isnt in VehicleSelctionGUI.Frame, reference it directly
    end
end)

Hopefully this helped!