My Exige is an 07, but built in 06. Perhaps your car is an 07, 07. There are a bunch of changes, bumperettes, maybe AC thermostat, and perhaps resistor pack. Or it could have been updated previously.
I would suggest mounting a replacement resistor pack in an accessible location. The nuisance of getting to it if anything dies makes it worth it
Look at the power connector, it is overloaded.
I used a fused relay and tapped power off of the jump start terminals for high speed, fan runs stronger and the high current path is all up on top where it is accessible. The only thing I didn't replace and I hope I don't regret it, is the power leads right to the motor. I saw someone else did this, making new leads right to the internal fan connections and kicked myself for not thinking of that.
In summary, I am suggesting:
replace the updated resistor pack with either real 100 watt resistors from an electronic supply house[not amazon] or 50 watts screwed to a .09"+ alloy plate as a heatsink
replace the wires all the way to the fan with minimum 14 ga wire.
cut that browned connector off and use the highest quality 1/4 connectors you can find.
If you want to get silly read my AC update thread: