I must apologize to several folks on this thread. I thought a cigarette lighter was a pretty simple subject. It appears it isn't so simple.
It is apparent that the 12 volt element will not get hot enough on half the voltage to fire up your Virginia Slim.
I just looked at my NAPA book and they have 2 full pages of lighters and replacement elements...all 12 volts. They did mention a manufacturer though..CASCO.
I did a search on E-bay using 'casco' and WOW, a veritable treasure trove of lighters.
There is a Casco lighter for a '53 Corvette going for $203.00.
I now know better than to shoot my trap off about Genuine GM Accessories...they are well researched and much coveted.
Stuart