I am not sure what 2005 Lincoln you have, but if it's a 2005 Lincoln LS like what the Curt hitch part # C12253 you referenced is designed to fit the answer would be "no it could not carry a 500 lb scooter on a hitch mounted carrier." The only solution with this vehicle would be with a small trailer towed with this hitch installed.
For trailer wiring you'd then need the part # C55373 which I recommend as it installs easily and is very reliable, and then for a ball mount # 36071 with hitch... view full answer...
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