73's use the long strap.
My sending unit works fine and I don't have the strap in place. I bought the short strap by accident and haven't gotten around to installing the long one. The sending unit grounds through the tank lock ring/tank/tank straps/body. This works when everything is nice and new but would probably stop working once surface rust starts. This is why the grounding strap is used. If you have a clean car underneath you don't necessarily need the strap. You could just run a wire from the sending unit body to the frame if you wanted to. That would accomplish the same thing.