Bad battery or Bad immobiliser

I have an Optima Yellowtop and I have turned SKS off for troubleshooting.

There are times when I open the doors get in and everything is dead. A few seconds later, the lights come on, I hit the start button and it fires right up. My Radio gives me a voltage check goes from 12V to 14.2V. I measured cold battery voltage this morning and it was 12.6V.

Sometimes, I pull to a stop, put in park hit the power button to shut off as I pull the fob from the ignition holder, the car powers itself back up. I end up holding the key in my hand and the car running in accessory mode. The CD player cycles and the clock resets to 1:00.

I pull to a stop, put in park hit the power button to shut off and it goes dead.

I come back to the car, open the doors, very faint bulb but car won't start. I suspect in this situatution that I got out of the car, walked away and the car has started up into accessory mode and drained the battery. At this point I connect the car to a Battery I have started carrying round with Jump leads. This boots the 12V system and allows me to start the car.

All I can think off is that I have a big short to ground somewere or a bad immobiliser.