First blip of the key locks the door but dash will stay live, It should go out and set the alarms eventually.
Second blip of the key should dump the dash lights and set the alarms immediately.
Try locking the car twice, wait a moment between blips. Try both at door lock (IR) and roof aerial (RF).
(Did this work?)
The back lights are only 1.2-1.5 watts each, far less than parking lamps, these alone cannot drain the battery, something else is doing that.