I think it's probably part of the security system, a hypothesis that's supported by the way that the power on/off key switch consists of just two wires.
Lets see what's inside. A bit of prying with a wood chisel and...
The back of this board looks a bit complex for just being a speaker driver.
Hmm.. lots of diodes, resistors, a transformer and an IC of some sort. Not sure what the IC is, but it at least drives the speaker, probably has the audio data that is played by the siren and arm/disarm in it's memory. Somewhere on here is probably a motion sensor as well, perhaps as part of the IC.. I could test that by hooking it back up to the harness, arming it and poking the speaker to see if motion triggers it.
Maybe later. I've just finished stripping the whole thing back down the the frame again. I'm considering ways to strip down the frame of the bike a bit to reduce weight and to combine it with parts from the kid's bike that I picked up.