Those are connectors for the backlights. Some people have found them to be finicky to extend, but you can try.
If it's an LED backlit monitor it might be better.
I knew they were for the backlighting, but I was wondering if that is actually some sort of generic connector that could be easily extended...
And what about these is so finnicky to extend? Should I know something before I pop the sockets off and solder on some more wire?