The origin is from the TV show Gilligan’s Island. It’s in reference to the redhead movie star “Ginger”.
Nonsense. “Ginger” has been a nickname for red-headed humans and chestnut (sorrel) horses for ever. It ties in with the spiciness of ginger root and the similar temper of redheads.
The OED gives the earliest documented use in this sense as 1785.
I can recall reading about the character "Ginger" Hebblethwaite, first appearance in Biggles and the Black Peril (1934), in the books by W E Johns and "Ginger" in Just William (1922) by Richmal Crompton, even before Gilligan was Maynard G Krebs.
Mericans: no sense of history.