Formula for power(in watts):
P=V×I. V is voltage. I is current
60 watts= 12 x 5, or 6 x 10.
If the wattage of the bulb is the same, twice as much current is drawn through a 6 volt switch at 6 volts. So theoretically a 6 volt switch is designed to handle twice the current a 12 volt one does.
I got an old VW 6 volt headlight switch, and I run LED headlights with no relays. They are bright as heck. 14 gauge wire is good for 15 amps. I might be running 3 amps.
Mitch is right.