The flickering LED that you show is NOT a direct substitute for a traditional incandescent bulb. Specifically, if you apply the specified DC voltage, a flickering LED flickers while a bulb will just be solid on. That is, there is a tiny electronic circuit built-in to the LED itself that modulates/pulses the LED to make it flicker. Likewise, you can buy LEDs that blink by themselves upon application of steady DC voltage.
So to make a bulb "flicker" to simulate firebox, the electronics generates a modulated/pulsed DC voltage. At least this is what the PS2 steam electronics does on the firebox light outputs. I am not familiar with the PS1 electronics.
In general, if you apply the PS2 firebox light output voltage to a flickering LED, it will not work because the flickering LED is expecting a steady (smooth) DC voltage. So there are various scenarios:
1) Use a pre-wired solid LED (not flickering). Then the PS2 flickering voltage directly drives the LED as if it were a bulb. There are some details such as matching the voltage which can be explored.
2a) Smooth the flickering voltage from the PS2 firebox output so that it's steady/smooth DC. Then use this to power the flickering LED. There are some details such as matching the voltage which can be explored.
2b) Smooth the voltage from a PS2 generic light output (could be headlight, interior light, etc.) so that it's steady/smooth DC. That is, there are some PS2 engines that do NOT have a flickering light output. But these outputs are nevertheless a pulsed (not smooth) DC. There are some details such as matching the voltage which can be explored.
3) There are some MTH engines where the engine lights are not driven directly from the PS2 board itself. There could be a so-called constant-voltage light board or the like. Such a board may already have a source of steady DC voltage which can be applied to a flickering LED. There are some details such as matching the voltage which can be explored.