Im working on my oil cooler system, while poking around in the engine bay, I seem to have pulled the wire out of this sensor, and I have no idea what sensor it is.

Oil level sensor is next to it. Its in the oil pan, so it must have something to do with oil, but iirc the pressure sensor is the big bulbous thing by the heater hose on the rear iron, so I have no idea what this one would be for.
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Cold Start

 

Oh good, its nothing to worry about. I dont even have the cold start system hooked up anymore.

 

Its the oil temp sensor for the cold start assist system. If you are not using the cold start assist it can remain in place with a broken wire.

 

If you use a 100w soldering iron, you can melt the material at the base of the sensor to expose whats left of the lead. Tin that lead nicely, cut back the wire that snapped off and tin it as well, slide on a short section of heat shrink tubing, solder them together and done. I'm unsure if the Oil Temp sensor is used for ECU fuel injection trim on an -SE, but I figured better to have it working than not. I don't notice any difference driving it, though.

Edit; checked the FSM and the Oil Temp sensor is not used for ECU fuel injection trim on the -SE. Its only mentioned as a Cold Start Assist trigger.