Dont panic its not as hard as it sounds
the reason for the 20A (might be 15A need to double check on mine) supply is because of the modern wiring looms in cars many now having built in Bulb failure monitoring which monitors the resistance caused by the bulbs in the event of a blown bulb the resistance in the circuit changes triggering a warning lamp on the dash often accompanied by an annoying beep (on my punto anyway)
So by plugging in a trailer the extra bulb now in the circuit alters the resistance and turns on the bulb failure system warning.. But it also protects the cars light control circuitry
and according to the tech at the local towbar supplier fiats wiring is thin (he drives an Alfa so is well aware of quirky Italian electrics
)
the 20A supply is used to power all the road lamps on the trailer Via a 7 way by-pass relay. The relay is connected to the light's +ve supply via a coil then to earth making an magnetic field closing the contact allowing the power from the 20A supply to flow to the trailer light. (if you dont know how a relay works sounds complex but it isnt really
http://home.howstuffworks.com/relay1.htm ) this only alters the resistance a tiny bit and therefore fools the bulb monitoring into thinking its working OK and rather than drawing the power off the lights supply the lamp is powered from the 20A supply the reason its a big supply is say your driving in Fog and you are about to turn at a junction, you have the road lights, fog light, brake lights and an indicator as you can tell this is quiet a draw on the cars electrics..
all that it involves in real life terms is the 7 trailing wires out one end of the relay (all colours match that of the trailer socket lead) to be scotched locked onto the light cluster loom (well 6 and the white one to earth) and the trailers socket 7 core wire fitted at the opposite end of the relay unit to a row of screw terminals (well 6 again and one to earth)
The reason they are classed as 7 way is the 7 way is for a reversing lamp on a caravan which is wired into a 12S (gray caravan plug) ((doubt you will be towing a caravan so dont worry about that)
Then the final connection to the relay is the 12v 20A supply which goes into another screw terminal.
the sounder for the indicator working warning is built into the unit so no need to worry about that..
IF i can find a scrap one in the garage i'll get you a photo up.... they cost about £20 in addition to the socket and wire/ scotch hooks
Dont be tempted to pull the supply from the cigar lighter as these are switched leaving you to need the ignition on to allow the hazzards/ parking lamps to work..