This connector is more to the right and a bit lower than the two in your photo with a brown and a white wire.
I got up around midnight because I was so pissed off with myself for disabling our only car.
I do have the two WSM volumes but finding info in them is never easy,
The volume with the wiring diagram and descriptions of the varying types of connectors, helped me to determine the connector I pulled the wires out of was a two wire to provide engine temp info to the computer so it can make some decisions. Brown wire and white wire.
The second WSM volume told me which wire was were in the connector.
I managed to disassembly the connector, then I soldered two small short wires to each of the brass terminals while it was on the work bench and reassembled the connector.
Finally, I stripped the two tiny wires in the wiring harness which had been ripped out. Soldered the ends. I think the term is "tinned" to just have each strand covered with a film of solder.
Having seen in the WSM recommended ways to splice wires to ensure you will not have a high resistance connection, I took a small crimp on electrical terminal and cut off the sleeve end where you crimp the bare wire. I stuck both wires into this sleeve and then crimped it to hold everything in place. Lastly I soldered the crimped sleeve and the wires so all were very well connected.
Feeling quite proud of myself around 2:30 am, I closed the hood and the car instantly started. Suddenly the idle was up and down, the engine was running very rough and kept stalling. The check engine light came on. I was really at a loss.
I opened the hood and luckily discovered the pcv hose I had removed to get easier access to the connector, had not been put back on.
Corrected that stupid mistake and immediately the car was running great but the check engine light was on. I was confident the light would eventually go off after a number of good cycles had occurred but I deleted the code (PO118) I think so my wife would not be worrying with the yellow light on.
The process of changing all hoses on our very high mileage car was a education. I had to go to Toyota to get the parts as GM had practically nothing. Toyota had two versions of the Matrix and by that I don't mean the base engine and the high output engine, rather some were made in Japan and some were made in the shared plant called NUMMI where Vibes and Matrix's were being built. Silly things like PVC valves and hoses were different on the same 2006 Matrix. On Amazon, I found molded heater hoses. I ordered both, one came in first in a small envelope so I knew there was a problem. When the second hose came in, small shipping envelope as well, what is being described on Amazon as heater hoses are actually, about 1/4" diameter hoses for the coolant circulating through the throttle body. The photos on Amazon gave no sense that you were looking at minaturized hoses.
I bit of trivia. The Tesla's are being built in the Nummi plant .