Parts List:
Resistors are 1/4W, carbon, 5% tolerance (or better).

R1 = 1.5K                        D1 = 1N4001
R2 = 1.5K                       BR1 = Bridge Rectifier or 4 1N4001 diodes
C1 = 0.1uF (100nF)              IC1 = 78L06, volt regulator (6V)
C2 = 0.1uF (100nF)        Led1,Led2 = LED, white, high brightness (Led2 optional)
C3 = 1F, 5V5 (GoldCap)         Led3 = optional.  Red (normal brightness) back light

Parts kit available.  No PCB!  [HeadLite Parts Kit]

Description:

Most irritating fact from most model trains is that the lights flicker when riding over crossroads, track-lane-changers, or lesser quality pieces of track.

This simple circuit stops all that. Even better, it ensures (within reason) that the lights are on constant, no matter what the speed of the train is (read: track voltage). On top of that the lights remain 'ON', for up to 5 minutes, when the train is not moving or parked.

Bridge Rectifier BR1 converts the AC voltage to DC. Even so, the BR1 (or 4 diodes) is needed no matter what, because the polarity changes depending on the direction of the train.

Thus, the 6VAC is presented at BR1, converts it to about 8.64VDC. From here it is regulated to 6VDC via the volt regulator IC1. This voltage is stabilized by using C1 and C2 of 0.1uF each, and reduced to 5.3Vdc by D1 (1N4001) which takes 0.7Vdc

The double-duty purpose of D1 is to block any energy from the GoldCap C3 going back on to the track when the there is no track-voltage present(train is idle, standing still, or parked). Hence the most important part of the circuit is the the 1 Farad, 5V5 GoldCap capacitor (C3) which is used as a storage reservoir for the reasons just mentioned. The GoldCap is available for values up to 22F (yes, F and not uF!). Because C3 is charged by the 78L06 with about 100mA max, the 1F type will take less than a minute to charge up.

The lights are fed from this GoldCap, best to use high-efficiency leds. A current of about 20mA per Led with the 1K5 resistor gives you about 5 minutes of light. If your train can handle the space, take a bigger cap for C3 so the lights stay on longer. Just make sure that the GoldCap's working voltage is not higher than 5.5V!

This circuit is excellent for some experimentation. With the 6 volt regulator and the voltage drop of 0.7V over diode D1, the working voltage for C3 is just under the maximum 5.5V (6V - 0.7V = 5.3V). With the 1F goldcap and the 2mA current through the led, the reservoir can provide about 5 minutes more or less depending if you use one or three leds. If you use high-intensity led(s), the current is a lot higher and the goldcap needs a higher capacity, something like 5F or higher.
I will make a pcb and layout when I have more time.

Have fun building this circuit and don't hesitate to experiment on it!