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Your didn't mention what year or what conditions you are talking about.
But, assuming it works like my l98's
If it's working properly-
It should flash when you open the doors while they are unlocked.
It should stay on steady when you lock the doors while they are open (arming the system).
If this is not what you mean, then i would first look at a bad ground somewhere in your system...
Where are the grounds located? Right now when I go out to the car, the security light is not on at all. When i open the door the security light then starts to flash.
Sounds like what started happening to my car just before the theft deterrent module went south. In case you need to locate it, it's behind the breadbox and a real futhermucker to get at. I'd at least check the connection at the plug on the module. It is a little more visible through the windshield if you take the dash pad off and have the lower hush panel off. Little black box. Once again, be prepared to curse a bit. It's in there but good. Let us know what you come up with!