I would use a piece of small 'enameled' wire from a transformer and thread it through a small brass tube and then use black heat shrink over the brass tube. this would give you 2 conductors to the light.
Any solid core, not stranded, wire will be stiff. The Romex stuff electricians use for house wiring is solid and I often use it for piping.wire with black insulation (or could be painted black) that is stiff
What does effective mean in this context? Thick enough to conduct power to something? Strong enough to stay in place? I picked an arbitrary number, as the Romex is usually 14ga plus insulation so it is way too big for our trains.find 18 ga as the smallest diameter that is effective?
I used hypodermic tubing to replace the handrails, the stuff they make needles from. You can buy 3 ft lengths on Amazon. Measure the diameter of the handrails and buy the appropriate size. Then buy some wire small enough to slide inside - the magnet wire will work. At the front, you can file an opening on the inside of the tube to bring the wire to the headlight.like piping from the headlight