Thing is, if you can't find a connector and separate it (which, all being good, should turn the fan on with the ignition), how can we tell you how to rewire it? It's like trying to teach a 5 year old how to defuse a bomb.
If I say I don't think it's the ECU, it's just me being an opinionated arrogant old bastard. But I'd guess that there are less than 20 people on the whole planet who know that ECU better than Woj, and that 15 of those work for Marelli -- the manufacturers. If he says it doesn't seem like the ECU, I'd take it very, very, seriously.
But, back to basics. For the motor to be on continuously it needs an earth connection -- a wire straight to the main earth on the driver's side inner wing will be fine, and a fused connection to a switched live. You can find a live that'll do the job with a 12v tester from Halfords, who'll sell you the cable, connectors and whotnot. 25 amps should be fine for the fuse -- they do in line ones. Do not attempt it without the fuse -- you stand a good chance of setting the car alight.
Just make sure that the switched live (goes off when the ignition is off) is a fairly substantial cable or it'll just burn out or pop another fuse. Something around 3mm thick will do.