I went out to my Mystique, the PATS LED does not blink with key on run position. I seem to remember the LED blinks with no cranking of the starter if the key is not programmed and you try to start. Is clutch pedal down when starting, I imagine so.

Did you just get new keys made? If so, try the others. This site has lots of (obscure) information about PATS
PATS from v8sho.combut no light blinks..