I'm not sure of the "laws" but I don't think DC voltage works the same as AC, where if you double the voltage, you halve the amperage. I converted my '61 to 12v pos earth and noticed that I blew an inline 5 amp fuse I had installed, at night, with the lights on, when I pressed the horn button. I checked my Alltette horn and it was drawing nearly nine amps. I adjusted the horn as best I could and although I could change the sound, I could not reduce the amperage. I then swapped it to my '54 Golden Flash (still 6v), and the horn drew 4 amps. My solution was to put in a 10amp fuse, no problem now. So in my case a doubling of the voltage, doubled the current drawn. I'm sure someone out there can explain this phenoma.
My reason for converting iin the first place was that my regulator was boiling my battery, so I wanted to use a Boyer regulator and my dealer suggested I change to 12v, brighter lights, easier access to bulbs etc. Can't say if it's so much better.
Clive