Stop in for a cup of coffee

You said the higher the voltage the higher the current? Hmm, Ohms law says otherwise...
That's how I used to think about it too. You know, like going to a 220 V AC motor from a 110.

The voltage in this case is the supply voltage.
P= IV and V=IR

Nominal 60 Watt lamp at 12 Volts draws 5 amps,
and so at 14 volts it should only draw 4.3 amps.

But that's wrong. :(

With a lamp and many other devices, resistance stays roughly the same, not the power.
Lets say that nominal 60 Watt lamp was rated at 12 Volts.
12 volts = 5 amps x R, R = 2.4 Ohms
then
14 volts = I x 2.4 Ohms, I = 5.8 amps

solving for the new power at 14 Volts
P= 14 volts x 5.8 amps
P = 81 Watts.

All assuming I didn't make a mistake.