Thanks for the reply.
It's the "Security indicator light". It's red in the shape of a car with a key through the middle. When the ignition is off, it blinks to indicate the security system is operational. In my case, the engine was running. The owner's manual says that if the light stays on with the ignition "on", the Vehicle Immobilizer System is malfunctioning and should be checked as soon as possible.
One other tidbit. When I picked up the car, the dealer didn't say anything about this, but when I got home and lifted the hood to check the fluids, I noticed that the red cover on the positive battery terminal was open. I suspect they had to jump the car to get it started (the door tag says it was manufactured 5/2014, so I suppose the car could have been sitting on their lot for a couple of months without being started).
When I checked the battery voltage today, it was holding at 10.5 volts, so whatever caused the original drain must not be doing so now. I didn't notice any of the doors ajar, but it won't be the first time I've not closed a door all the way

I'm hoping it's just a bad battery, but I'll post whatever diagnosis I get from the dealer tomorrow.