Hello Techie, you are correct, after a lot of digging I have found that these connectors are two pin JST wire harnesses that power the CCFLs. They do not use basic wires , they use silicon wire which is insulated better and carry any were from 700 to 1400 volts. I am going to post a picture of the broken wire, which in all honesty is my fault. I ripped the wire from the connector when trying to unplug them from the inverter board, it was extremely hard to get the connector out with the ripped wire while the others were easy.
Also to answer your question to what problem I was having with the monitor. It was the two seconds to black problem that I know a lot of people have had with this monitor (Gateway LP1925 HD1900 19'' LCD) I have come to the conclusion that it must be one or more of the CCFLs. I have checked all the readings on the inverter board with a multimeter and everything checked out okay. But then again I could have missed something and I will not be entirely sure until I get an extra CCFL and check the lamps.
This is the broken wire on the connector not sure if it would be better to just buy a whole new set of connectors and wires.