I want to have multiple players able to move their own objects along the rail (on a touch screen device), so I won't be using the mouse object.
I also want to have the object actually move along with the player's finger, perhaps with a bit of leeway so it can continue moving even if they get a little ahead of the object itself (I could do an "Is touching object", but the movement stops immediately if the player isn't right on top of it the whole time).
I think your examples with the two circles is pretty helpful if I make the size difference very minimal (I really want zero forward or backward wiggle room...only sliding left or right down the "rail"),