Never had a Fiat that didn't put the lights off when the ignition was turned off.
If you required parking lights with the 500s we had with BSM, 2009/10, you had to turn the lights off, then on with teh ignition off. That gave sidelights. I think the Panda may do something similar, but in 10 years, have never had to park with lights on.
Edit: Just looked in the handbook.
"PARKING LIGHTS fig. 51/a
With the ignition key at STOP or removed,
turn lever to position 6. The instrument
panel warning light 3 will
come on together with side/taillights and
number plate light.
Move the lever upwards a to turn the
right-hand sidelights on only; move it
downwards bto turn the left-hand ones
on. In both cases, warning light 3will
not turn on."