By disconnecting the connector this caused the computer to go into protect mode turning on the fan.
You may need a connector a sensor or both.
By wiggling the connector you may have just interrupted the connection causing the fail safe mode. (this being said the connector should be able to tolerate a fair amount of wiggling without interruption)
however since I am not there to watch how hard or vigorous you were tugging on the connector it is likely that the connector could be corroded,the female wire connections could be worn.
The rubber seal could be missing and the plastic locking tab could be gone.
Does the fan come on with the A/C?
your problem could be a number of things, from a stuck thermostat, air in the cooling system,coolant without the correct ratio coolant- distilled water, a leak in the cooling system, the sensor and or connector. ETC
start with the basics, check the coolant level and mixture ratio, ( with a tool like the one provided in the link )
http://www.napaonline.com/Catalog/C...Shield-Balkamp-Inc-/_/R-BK_7761025_0438142340
Pressure test the cooling system and repair any and all leaks also test the pressure cap. fill the cooling system with the correct mixture coolant-distilled water and bleed the system.
If your unsure about the thermostat replace it with a OEM or Stant thermostat or you could test the thermostat by putting it in water heated on a stove with a calibrated temperature gauge and confirm it opens at the correct temperature.
Then connect a
scan tool with live data to confirm the engine coolant sensor is reading correctly while your in there check for codes.
If after this work has been completed and your still having a problem you will want to follow the diagnostic steps in a factory service manual to diagnose the engine cooling fan.