James,
That wire might be the "aerial" used to pickup the code from the fob.
When the alarm goes off you can diagnose what caused it.
If the alarm goes off it will emit three beeps as opposed to two when you disarm it. If this happens the LED will flash a code telling you what set off the alarm.
The flashes indicate the following:
Movement sensor - 1 pulse on, 3 second pause
Negative input or loop circuit (usually under the pillion seat) - 2 pulses on, 3 second pause
Ignition sensing - 3 pulses on, 3 second pause
Self powered (12volt supply removed) - 4 pulses on, 3 second pause
You can find full instructions for this system
here.