Script makes everything beyond "Right" invisible, Any help?

It's not clear exactly how you want it to work, but I will assume like this: The event occurs, then Right disappears, and Right1 will disappear then reappear after 1 second. Then Right2 will disappear and reappear after 1 second, etc. Right will reappear after everything else.

If this is the case, you simply have things out of order. Your wait(1) should be between setting the transparency to 0/1, instead of between objects. Also, you should set transparency to 1 (invisible) first, then set back to 0. Doing it the way you have it (other way around) will make them visible first, then invisible after, resulting in every part except Right to be invisible in the end.

The correct script would look like this:

function onClick(player)
    -- Make 'Right' invisible
    player.Character.Right.Transparency = 1

    -- Make 'Right1' invisible for 1 second, then reappear
    player.Character.Right1.Transparency = 1
    wait(1)
    player.Character.Right1.Transparency = 0

    -- Make 'Right2' invisible for 1 second, then reappear
    player.Character.Right2.Transparency = 1
    wait(1)
    player.Character.Right2.Transparency = 0

    -- Make 'Right3' invisible for 1 second, then reappear
    player.Character.Right3.Transparency = 1
    wait(1)
    player.Character.Right3.Transparency = 0

    -- Make 'Right4' invisible for 1 second, then reappear
    player.Character.Right4.Transparency = 1
    wait(1)
    player.Character.Right4.Transparency = 0

    -- Make 'Right' reappear
    player.Character.Right.Transparency = 0  
end

script.Parent.ClickDetector.MouseClick:Connect(onClick)

Hope this helps! :)