You said in first post that the Bell activates when you removed the power from the bellbox. - So it seems to be self activating ok.
That then suggests the trigger from the panel is not working right, either bad connection/short between trigger and -12v (for negative tamper) or perhaps bell is set for neg trigger when panel is positive (or vice versa - though perhaps more likely to have a constantly wailing bellbox if this was the case, I've never tried this, either accidently or on purpose).
You could test the trigger in the panel with a multi-meter to check its changing/sending correct signal when bell activated, however thats assuming that you installed the panel and are confident opening it up and using multimeter.
CDJ