I have had this issue along with a few other issues; the climate control would not turn on properly, cruise would not work and it wouldn't start sometimes. All things described were sporadic and intermittent. What ended up fixing it was putting in a new ignition harness. I found one online at Rock Auto for less than $40. My local NAPA store wanted over $80 for this. The repair was fairly easy but involved tearing the dash apart.
Everything now works as it should and no more security light on.