UPDATE: I needed to add a "keep alive" capacitor. Even with both trucks wired in parallel and perfectly clean track, wheels, and rollers, there was still some flickering. I added a 1000 MFD 25 VDC electrolytic capacitor in parallel with the string of four LEDs.
Here is the final schematic:
Here is the same thing in a sort of wiring diagram. It shows the physical connection points for each truck's wheels and rollers and the added wires running along the length of the car.
A photo of the plastic bar that has the diode, resistor, capacitor, and two of the LED's. The other two LED's are on the bar at the other end of the car. This is a rather crude assembly, but it is effective.