The thing that is not immediately obvious in the video: you have to push the connector IN to the housing from behind the connector to relieve the tension on the small latch that the pin has before you try to release the latch with a pin from the inside. "Too thick" or "too thin" does not apply here: pulling on the wire as you try to release it with a pin from the other side of the connector makes all the difference. I have successfully used a fine screwdriver, hatpin, copper wire, needle, etc. and been successful each time.

The key here is BE PATIENT and DON'T force it, or you will never get it out.