I tried powering with the 14V AC from a Z4000 via a bridge rectifier. The module never quite powers up and has all digits-segments on dimly. But by placing a 1000uF capacitor with proper polarity on output of bridge rectifier the module powers up correctly flashing P1.2 about 3 times then goes to 000 ready for action.
That is, a bridge rectifier by itself generates choppy DC that I don't think the module likes. The capacitor smooths it out. I was reading about 16V DC at the module (with the 1000uF capacitor). I used 1000uF because I believe you may have some lying around.
Your 12V 2A adapter definitely appears screwy if DC voltage is hopping around!