Does anyone know how to re-solder the green paper behind the instrument cluster????

 

That green paper is called a printed circuit board. Soldering really depends on what the problem is.

 

I'm customizing my cluster, but I need to cut a hole where 1 of the plugs are going, so I was wondering if I could solder wires to where the connector should be and attach wire connectors to extend to the stock harness plug

 

You have to be very careful. The best thing to do is connect where the factory did. If you can't, first peel off the coating over the conductor. Apply liquid solder paste to the spots you want to solder. Tin the wires you will be using - use small dia. multistranded wire. Using a low temp iron (500-600) and good quality small dia. solder, hold the wire to the pad and touch it with the iron, just long enough for the solder to flow. Test the joint. If it's stuck, then attach the wire to the board with "Electronics grade" silicone rubber to ensure it will not be pulled off - I'm not talking of just on the joint, but rather about 1 cm down the wire. Don't apply the silicone too thick, 1/8" max or it will not set up for days. Leave it overnight until the silicone rubber has hardened.