Thanks John.
On this engine, the resistor is simply lying across the smoke unit "bowl", with the ground end soldered to the unit's mounting frame and the other soldered to the hot lead; no circuit board.
FWIW, I changed out the power pack to a Troller "Autopulse" that puts out only max. 12 volts; the smoker is still putting out well when the pack is set at about 8.5V, so perhaps I'll be buying some time to the resistor by doing this(?)
Mark in Oregon