Right mate ..

The Alternator warning light has an ignition fed supply (in the console) to one side of the light.
The other side of the light connects back to the Alternator warning light output .. It could have been botched by connecting somewhere else .. but the Alternator terminal is where it should be connected.
When the alternator produces a charge, this will then give you 12v on each side of the warning light, yes? Now a lot of folks dont understand this bit .... The bulb will go out, cos no current is flowing.
If the Alternator fails, the regulator inside usually earths (or partially earths) this side ... so you get a light on. So earthing this wire also puts the light on.

If a heated screen has been added, the trigger wire to the relay should originate from the warning light terminal - It's actually spliced inside the car on the way to the dash warning light.

You need to weigh up what you actually have in place; Is that blue wire connected to a thick cable or another (blue) thin one?