Stop in for a cup of coffee

Mattax said
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.

I always though about light and voltage this way...

Higher voltage means more electrons per unit time that can be converted to photons.

Amps determine how fast the supply of electrons can be replenished (or sustained at steady draw rate) to maintain the photon emission rate (luminosity).

In other words, higher voltage means more photons (light output) as long as it is not restricted by resistance to amperage flow that chokes off the electrons being converted to photons.