Tha DP alarm is actually a Spyball Patriot. BTW.
Yes the immob is automatic - signified by a quick flashing warning light.
The alarm is activated (as you say) by the LH button.
After u press the button it takes 1 min to arm - during which time u should see a constant red light, at the end of this period it should change to a slow flashing light, signifying the alarm is set.
If the alarm sounds at the end of the 1min arming period you have a fault!! but you knew that anyway
IMHO the most likely causes are:
1/ water in the alarm or associated loom,
2/ there is a microswitch with a thin metal arm that protects the alarm from tampering. When the body panel over the alarm(wherever it is) is removed, it trips the switch, a failure here will cause the fault u have - believe me I know!!
Have u taken off the fairings and bent this arm by accident?? Its quite easy to do.
I have a copy of the alarm instructions,
which I will try to copy if u like?