Yes, it's normal. In Europe, you must always have the off side parking light lit if parked in a residential area where the vehicle is not clearly visible at night. It is also a requirement here, but generally not enforced. I mean, can you imagine the police patrolling at night to catch offenders? ONLY KIDDING.

Now, I believe this only happens if you park where it is dark. When you take the ignition key out, you should get a warning tone sound.

The current draw is not that great because it only lights up two parking lamps that are 5 W each. If you left the light switch with the parking lamps on, then you have 4 parking lamps, plus 2 number plate lamps at 5 W each.