Start with a radio controlled car--one where the wheels stay engaged with the motor. Some of the cheapest cars have a slip arrangement in the gearbox for changing direction. We need a vehicle which is either tank like (left side on or right side on) or one with geared drive wheels and proportional steering. I've suggested one from Amazon.com that works.
Remove the cover and the lid to the battery container.
Remove the springs from the battery container.
Separate the car by removing screws so that you can access the motors.
Notice that two wires go to each motor assembly from the electronic unit (green, yellow and red, blue).
Cut the motor wires from the electronic assemly (radio receiver) and save the receiver for a future project.
Drill 1/8 inch holes in the battery compartment and clip out one of the battery separation walls.
Bring the motor wires through the holes and refasten the housing to the wheel assembly.
Create a diode bridge (see schematic in step number one). This allows voltage generated by the motor assembly (dc motors act like generators when turned) to always come out in a predictable fashion, regardless of which way the motor (now generator) is turned. I use a diode bridge for each motor assembly so that they will feed the capacitor and led rather than each other.
Solder the motor leads to the input of the diode bridge (the place where head and tail of diodes meet).
Insert two pieces of double sided foam tape to the ultracapacitor.
Stick the ultracapacitor into the battery compartment and bring positive and negative leads from the diode bridges to the capacitor.
Prepare to insert the led to the roof. I tried to drill through an existing "light assembly," but the drill bit caught and spun the assembly off into some unknown corner of the garage (this is why I wear goggles--you can never be sure when something strange is going to happen).
Having lost the light, I designed and printed a "light bar" with a 3d printer.
DO NOT ATTACH LEDS OR ANY SMALL PARTS IN A WAY THAT THEY CAN COME LOOSE IF THIS TOY IS TO BE USED BY A SMALL CHILD.
Sorry for "shouting," but this is important.
Drill holes in the roof and attach your led assembly to the roof. Bring the led wires to the capacitor. Put electrical tape around the diode bridges; we don't want things touching and shorting out.
Secure all the parts and give it a test run.
You will have to pull it a few times to charge the capacitor--then the light will stay on for quite a while (actually will glow for a couple of hours).