you should have three wires comming out of your mirror:
violet/white is your +12v switched. Connect that to the violet white on the courtesy light.
Brown is earth, goes to brown on the light.
The blue/yellow is suppose to go to your reversing light switch so the mirror wont dim while your reversing - as if anyone uses the mirror to see where there going while reversing
. Personally,I'd leave this wire unconnected but if you want it to function as designed you'll have to connect it to the +12v comming off the gearbox reverse sensor.
If I was doing this I'd use scotchloks to make the connections, saves pissing around stripping wires & soldering.