I found the section of track that I used in previous thread - it has isolated "islands" each with an LED.
To generate the random effect, I used the solid-state cycle-timer module I showed earlier. The timer module was programmed to cycle on-off with 2 different "duty-cycles".
In the first demo, the module cycles 50% ON, 50% OFF every second. So 0.5 sec on, 0.5 sec off, repeating forever. So when an axle sits on a trigger island, the LED will blink 0.5 sec on, 0.5 sec off.
In the 2nd demo, the module cycles 10% ON, 90% OFF every second. So 0.1 sec on, 0.9 sec off, repeating forever.
So when all's said and done, the 50% ON should "spark" 5 times more often than the 10% ON. The module is programmable so you can mess with the ON-OFF ratio to adjust the effect to your liking. It is not a truly "random" effect but might be good enough.
In the measure-twice, cut-once category note that the left trigger island is maybe 1/2 the length of the right trigger island. This is also an adjustable parameter as a longer island has a greater chance of triggering...but obviously it's easier to re-program the timer module than to re-cut islands!
If this approach shows promise, I can draw up wiring instructions. Let me know how many trigger islands you plan to have, and any other electrical related info such as track voltage, power available, LED components you're looking to use, etc.
