Been swamped with the big charger.
You need to measure and compare where the slider is
How bright the outside light is
In volts. With a meter.
Some of the 5mm and 10mm LEDs I work with have a surprisingly low voltage threshold. i.e.
They light up at a very low voltage. And they have a resistor in line right from the factory.
I cannot imagine an incandescent lamp being used -- useful at five volts. But then I am not there to see it in use.
You will need to access the power wire at the outside bulb when the bulb is in place and glowing. I am assuming this is not a tight PWM control module and load ballast will affect voltage -- so the bulb must be glowing to get an idea of what is happening with the voltage
Armed with voltage stats I can access my supply of LEDs and then power things up on my bench supply. Then perhaps give clues where to buy on eBay. An angry 5 or 10 mm LED puts out too much light for pilot duty anyway.
The LED would then be connected to the outlet of your circuit board meaning from the + and - wires which are easier to work with.