Do you have a wiring schematic and is the new harness a direct replacement with the same style connectors? The best way to do it is to compare your stock harness to a schematic and then look at the new harness wire by wire to find your differences. The wiring may have the same colors but may be in different spots in the connectors. This is a little time consuming but some companies are not very good at keeping original color codes. All it takes is one or two wires out of place to cause a big headache...
'04 Mazda RX-8 GT, 6 port 13B Renesis, CAI, 6 speed, 4.44:1 LSD.