If you turn that PCB, I think you have some real-estate on the back side to add some kind of electronic trigger to activate the flickering action. That is, I don't think you have enough capacitance on board to directly drive the board from the narrow-pulsing PS2 lamp signal. Specifically, in the case of PS2, I figure you'd want to turn on flicker at the same time as, say, the Cab Lights, Headlights, or whatever. So the board would be powered by track AC or even DC-PV...and then the pulsed lamp signal would trigger the actual flickering via some 10 cent trigger circuit. Now one could argue a prototype firebox would be active hours or days before and after an operating session so flicker might be visible even when engine is not ON!
Anyway, I'm imagining other applications where flicker is intermittently active and activated for brief periods by an external control signal that may not have enough current to drive the entire circuit. This trigger signal might, for example, be an Arduino output pin. Layout applications might include, say, welder flicker in an engine shop.
Here's an application from years ago before the benefit of low-cost flickering LEDs. In fact I used xmas string incandescent bulbs driven by a custom pulsing circuit. If I had a flickering circuit board that could be triggered by a low-current control signal, I would probably have used that. Note the coincidence that, like your 4 LEDs, 4 incandescent bulbs were needed/used to give the "variety" of flame simulation.
The video also illustrates how sound goes hand in hand with the "visual" animation. Fires are noisy affairs!
To wit, the old-school way for fire/flame simulation was to hook an incandescent bulb to the speaker of an AM radio tuned to an unused station with just the "static" crackling sound. The bulb would flicker and the crackling sound provided a reasonable facsimile of a fire.
