I think we need more info on exactly what he has. A closeup photo of the board's components would be useful. If these modules only use 150 mA with horn...I'd think it much less with just the prime mover sound which I'd think relaxes the stored energy requirement. That is, is it required to maintain sounds while simultaneously pressing the Horn button and the Direction button?
Anyway, if the stored energy requirement goes down to a fraction of a Joule, it almost becomes practical to just crank up the electrolytic capacitor (a few more thousand uF) rather than messing with a super-cap.
Not trying to get too far ahead of myself, but we know the processor in this module must be measuring the track voltage since it has to detect DC offset voltages to trigger the Horn. I can imagine a design where that same function simply turns off the audio when track voltage is lost for some period of time...rather than letting the drooping voltage cause funny audio thumps, clicks, or pops. In other words, wouldn't it be annoying to add a super-cap to keep the circuitry running but the software on the board has already shut-off the audio output because it has detected a lack of track voltage! 
