Wow. Someone reading this thread is going to be more confused then when they started. I am going to add my own thoughts just to make things worse. A lot of good products are mentioned, but they have to be used the right way and a lot of time these posts don't explain that.
First, nine times out of ten the connector is not stuck, you just haven't succeeded in disengaging which ever diabolical locking device Toyota engineers installed on that plug. This is not a shot at anybody...I am talking about my own experience. Make sure you are doing it right, and not trying to separate something that is really one piece. Go get the right tool you were too lazy to look for at the beginning and really squeeze that locking thing and don't get blocked by any ridges on the side and try again also using the right tool to separate at the same time. Get help if you need it. Sometimes it just takes three hands. Usually, it will amaze you by how it flies apart when you find the secret.
If it really is stuck, (rare) I will use a penetrant like PBBlaster to help get it apart. Then, clean the contacts with DeOxit or CRC Contact cleaner or whatever and blow it out with compressed air. Do it again if it needs it. Then dielectric grease on top to protect it. Do not use conducting grease unless it is a ONE wire terminal, like a car battery. Then you can use Fluid film, Vaseline or terminal grease or whatever. I use Vaseline. Dielectric grease does not interfere with metal-to-metal connections. Don't listen to anyone who says different. I've been using it for forty years.
