An excellent source of carbon rods are the center posts of any standard disposable AA, C or D battery! (ever wonder what to do with all those "useless" batteries in the Aftertime?). I remember hooking a pair of these rods up to a 12 volt model train transformer when I was a kid, just to see the show. Keep in mind that the other compounds in the battery are caustic, so keep them off your skin and be sure to wash the carbon rods off before you handle them.
The result was light. Remember the old carbon arcs were used for movie projection systems for years, since it was the only source of light bright enough at the time.
All I did was wrap the tips of exposed doorbell wire around the ends of the carbon rods and plug it in. The proper gap needs to be maintained between the rods to get that brilliant spark, and it may not be like the movie theaters at only 12 volts, but it was light, beautiful bright white light. Puts off some smoke, but I did this in a bedroom without running everyone out. Remember I was only 12 or so, and that was a long time ago. I doubt it was enough light to compete with today's metal halide bulbs, but it was light sure enough, which beats the heck out of darkness. Need some kind of feed mechanism to adjust the gap, but this could be two blocks of wood with holes drilled to hold the carbon rods adjusted by hand if necessary.
Offered by Ron.