is the light by the P on the shifter supposed to stay on after the car is off and armed?

reason being i think i have a short or constant current draw cause my battery keeps on dying and im not sure where to start. i am going to change my battery this weekend to see if it also helps.

For 16 minutes. If its on longer than that, you've got a problem. The LED itself does not draw enough to be the cause.

Yes, this is a oft asked & qnswered question. The light next to the "P" will stay illuminated for approx 15min then go off (as long as the door handle nor buttons on the key are pressed).

As soon as the door handle is lifted or the buttons on the key are pressed, the car will come back to life, in preperations to react to what ever the driver is going to do.

BTW, you asked and posted this same question twice...and got a reply to both. Feel free to delete this one...just follow thru with clicking the appropriate boxes & links