There are no gnomes in Swords & Wizardry, just tantalizing hints...
White Box (3rd)
Dwarves can speak gnomish (page 16)
White Box (1st)
Halfling is a broader category of wee folk, including gnomes (page 10)
There is no entry for Gnome, but they are mentioned in some of the encounter write ups - beware of spoilers. A type of armor is described that specifically calls out sizes for halflings and gnomes being smaller than dwarves (page 14). Officially gnomes use halfling stats (page 66, 70). Most telling, a couple of entries outline the gnome village of Nomengarten. We get all the standard fare, including mushroom houses, earth-tone clothes, red, cone hats, peace-loving friends of small forest animals (think Pink Floyd), smurf-like singing and dancing, gold and pastries. I would also add that gnomes seem to attract a certain category of monsters...
Finally, here is a thorough exposition on the broader subject by Matthew James Stanham.
And this is just genius: The Backpack Gnome by tony dowler