2004 security system dash light

[What have I don]

I have a 2004 Silverado half-ton, extended cab z-71. It has the factory auto lock and alarm. Over the last 3 days I've noticed that the yellow security/alarm light on the left upper area of the instrument pod with a continuous, soft illumination, even when the ignition is off. It occassionally pulses, although this is barely perceptable. The lock/unlock and alarm features all work appropriately, with the suspect light brightly illuminating when the key fob buttons are pushed. The red radio LED also blinks appropriately.

Obviously, I'm worried about a short that could eventually drain the battery. I would'nt think this is a bulb problem, since power is getting to it even when the vehicle is not operational. Could it be a relay? If so, where is it? Is there a ground point for this? if so, where?

Any advice would be greatly appreciated!
Thanks

[NCroadracer]

sounds like the instrument cluster is the culprit. A complete lack of any security related symptoms and knowing the clusters for their sporratic failures... i'd say it's a safe assumption that the cluster is in its early stages of failing.