I remember my Father, who passed away in 1970 often commented on seeing a horse with rider doing a "single-footing gait". Anyone ever heard of this gaiting foot fall sequence? Could have just been an old time term for a gaited horse. It was after all a LONG time ago. My Father was born in 1910.
The North American Single-Footing Horse is a legitimate breed with a breed registration, unlike the National Racking Horse Association which registers any American Saddlebred or Tennessee Walking Horse.
In Easy-Gaited Horses it's listed the other way - Singlefoot as slower and rack as faster. Which, yeah, doesn't make sense with the name. But the basic difference between the two is 3-foot/2-foot support at the slower gait and 2-foot/1-foot support at the faster gait.