If you turn on the passenger map reading light (there will be 3 lights near the interior rear mirror, left and right are the map readers) and lock the car, the light should go oft. If it doesn't then one of the relays is staying on, supplying power to the car when it shouldn't.
On an older car like the FL1 the key turns to move a switch which appliies or removes power to a lot of the electrical items on it.
In a more modern car like a FL2, most of the cars electrics are powered in stages. When you unlock it, or put the "key" fob in the dash, or press the Start button.
If yer interior passenger map reading light stays on when the car is locked by the remote fob, then it means the computer hasn't told one of the relays to turn oft. Or more likely the relay is broke'd and staying on by itself.