I'm not sure how the Triumph alarm is set up but some alarms have an internal battery and will go off when the main battery is disconnected as an additional deterrent. If you have a charging issue or a bad battery then this could make the alarm "think" that someone is trying to get around the alarm by disconnecting its main power source. I understand your desire to keep the bike relatively safe by installing the alarm but I have to say that I haven't heard a lot of good things about the OEM alarms working nicely with our bikes.
