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It's normal (at least it is on my '96), assuming the engine is off.
It is just a reminder to lock the doors using the power lock switch. If you do that the light goes on solid (and the alarm is armed). Disarm the alarm by unlocking the drivers door from the outside the the key.
From: 1994 LT1 Coupe 6-speed with FX3 & 2000 LS1 Vert 6-Speed with F45 Hunterdon County, NJ
The blinking 'secuirity' light means the alarm has not been setting --
either the PKE 'passive' enable feature is turned off (check owners manual),
or
your door switch(s) are not telling the BCM the door door has been closed and to allow the alarm to be enabled.
FYI, the door switch(s) fail either mechanically (stick), or their 'nose' is pushed-in all the way so when the door is closed, they are not pushed in enough to electrically disconnect the circuit, or they just fail electrically to connect the circuit when fully extended.
P.S. if the door switch has died, it can be replaced right through its hole, without requiring taking the whole door apart.
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