Shift Interlock lag...

Putting my car into park, it seems to take a few seconds before it registers as being in park, to allow me to remove the key... I don't do anything during this time, just the [ P ] indicator on the dash doesn't light up for the few seconds, then when it does, I can safely remove the key... If I try to before hand, it only goes as far as the accessory mode, but I can't remove it further than that.

Just started happening, which I've attributed to being too cold out.. but that's only probally part of the problem (cold makes something already wrong worse --- Shifter had stickiness pulling though [ R ] before, this is an automatic transimssion. )

Thanks for any advice or idea what it is, and best way to deal with it before bringing it in (wd40 somewhere? ;P)