If I can get my hands on the alarm device, I would take it out onto a bench and use some electronics test equipment to diagnose what had gone south and see if I could repair it. That, or get a replacement unit and swap it in.
The dashboard deconstruction project is allowing me to fix other little issues that have bothered me, but so far I have yet to chase where the alarm LED wire goes to, besides off into the guts of the dashbaord.