Chosen Solution

I hardly ever use the laptop, so I don’t care if the fan is always on. This part had been broken for years Update (01/10/2019) Thank you for trying to help. I will try to upload the picture

As it turns out you can fix this quit easily! You’ll need to clean the logic board a bit as you have some junk (glue?) which needs to be cleaned off. Getting a replacement socket soldering it down, and getting a replacement fan is all you need here. Molex connector, header P/N 78171-04MacBook Pro 13" Unibody and MacBook 13" Unibody Fan

Typically each connection is report to the operating system as functioning or not. The connection breaking off the logic board could prevent you from running the system all together as wiring it through another connection point is going to still fail to report that specific fan from being reports and would likely cause potential kernel errors and crashes due to the systems desire to protect the logic board components with proper ventilation.

In one of my bright moments i ordered a while back thermal paste, conductive glue. It came all the way from China as someone sings so beautifully. It came in a seringe and a needle. I am living in a nursing home, so i dropped it on the table where i was, in the activities room, and screamed that it wasn’t mine. The administrator of the hospital researched it and i had forgotten that i did order it. It said nothing about what it was inside. In a junkie family someone could have hurt themselves. Anyway, would such glue work? I think fans like to eat amperage, so i never tried.