Here's a small picture (all I could find) of a modern unit used to start fires by igniting a soaked or covered stone on the end of a rod. Same idea, but a small compact modern model which holds less fuel as a safety factor I would imagine.
Firelighter Wet Stone And Rod
"The black, cast-iron pot measures 8" high X 5" wide. The pot is used to contain a non-volatile fire starting fluid like kerosene that soaks into the stone on the end of the rod. When the stone is removed from the pot and placed under your logs it can be lit with a match. The stone will burn about 10 minutes - long enough to set a good blaze."
The "wand" in your older model was perforated to allow for a larger coating of the coal oil to adhere on both the inside and outside surfaces. One would shove the wand into the starter wood and ignite it. When all of the fuel coating the end of the rod burned off you should have a good fire started allowing you to pull the wand out of the fireplace.