Yesterday I got a message when I started the engine that said something like, "Service needed", so I put my OBDII scanner on it. No faults. I disconnected the scanner and did the double lock sleep procedure I've always done in the past after scanning.

Fast-forward to an hour ago when I took the F-Type to Costco to get some supplies. When I started the engine and put it in reverse, the little beep beep horn that tells you when your door is locked did a double beep. Then it did it again. I stared rolling backwards and it did it again. I put it in drive, and the fourth beep beep. It never did it again. I double locked the car at Costco, and it didn't do it when I came back with my stuff to drive home, however when I parked in my driveway and put it in Park, the engine quit on its own.

Any ideas???

 

The service message is probably just due to time/mileage since the reminder was last reset. Even if it's been to the shop, they sometimes forget to reset.
You can reset it yourself:
1) Set ignition on
2) Open hood
3) Open driver's door
4) Fully depress both accelerator and brake pedals for 10 seconds
5) Turn off ignition
If the message still appears, try again.

The double beep can also be because the car thinks something is still open (door,trunk,hood), although you should see a message. (It can be caused by a bad sensor, but should still generate a message.)

Last thought is battery / charge. The most common cause of false messages is power related. Older batteries, discharged ones, or even new batteries (that often aren't fully charged). Put the car on a CTEK and let it run overnight. If your battery is several years old, go ahead and replace it while it's convenient. You can get a fitting Interstate at Costco.

You mentioned having a scanner, I assume you've heard that they need to be properly disconnected; otherwise the battery will drain. Briefly disconnecting the battery will reset the system.

 

As Uncle Heel says (I have a Tarheel friend, so know what you mean, but my mind always reads it that way) I would think the double-beep means something is not closed properly, but that there should be an indication on the dash.