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Generally wires of those colors have three assignments.
In this case, it is partly uncertain.
Do those wires go to a power plug? or do they go into the circuitry of the gelato maker?
Depending upon which way they go, their assignment by color could be different.
- If the wires go to a power plug (and the switch is a power switch) then the white is 'hot' or voltage-dangerous. The black might be the neutral prong and the brown the ground, or the black might be ground and the brown the neutral prong.
Ground, where a power plug is concerned, is easy to tell: it's the wire that goes to the third, round, prong of the power plug. (And of course, the narrow prong is the 'hot', the broad prong the 'neutral'.)
- If the wires go into the gelato maker's circuitry, that's different... and the color coding could mean anything.
So what is the switch? why is it disconnected? what do those wires lead to?
This is a tentative answer, for now.