"Pop`" writes:

So yes, a 12 volt lamp will work on 6 volts (if power supply can
provide sufficient current). Just not work very well.

NO, it will not. There will be insufficient heat in the element to provide
any light or even a glow with a 12V bulb at 6V DC. A 12VDC bulb will begin
to dim substantially at 9 VDC and may not even be visible in the light of a
room.

A counterexample: I just connected a 12 V automobile headlight lamp
(the high beam filament of an H4 lamp, rated 60 W at 12 V) to a bench
power supply. The power supply current limits and can't raise the
voltage above 4.8 V. At that voltage, the 12 V bulb is definitely
glowing. It's reddish rather than white light, but it's unmistakably
glowing. If I reduce the voltage further, I can still see a dull glow
at 1.5 V, one eighth of the rated 12 V.

At 6 V, it would be whiter and brighter, but 4.8 V is enough.

Do not profess knowledge you do not have.

So, what bulb did you test? Which 12 V rated bulb does not light up at
all at 6 V? Surely you tried it before writing?

Dave