2001 Ford FOcus zx3 cooling fan turns on too late, how to fix?

My wife has a 2001 Ford Focus zx3. Usually the car runs cool enough to have no observable problems, but on a hot day in stop and go traffic, the cooling fan will not turn on until the temperature gauge starts to get a bit too close to the red (not in the red though). My wife says that keeping the air conditioning turned ON stops this from happening (this sounds a bit counter-intuitive, but maybe Ford has it wired this way to counter the extra load on the engine from the AC?). The check engine light has since turned on and I am almost certain it is because of this. Perhaps it is triggered by hitting too high of a temperature?

Also, if anyone knows these cars really well, there is an electrical connector on the plastic piece that covers the cylinder head, almost directly behind the transmission dipstick (it looks a bit like an oxygen sensor, but is in the wrong place to be one). I noticed when I was looking at her car that there is no wiring connected into this piece (it looks like there should be though). Perhaps this is related to the cooling fan issue?

Any ideas or relevant information would be greatly appreciated. Thanks so much.