rewiring a basement light
Rob, thank you for explaining what you are doing, but I got that from your original question. What you need to do is re-wire the complete lighting arrangement in your basement. 

My suggestion is to remove what's there and put in exactly what you need in each room/area. If you do not know what to do this wiring please simply hire an electrician to do this job for you. 

If you are making this into bedrooms there are several other VERY important codes you MUST follow, such as AFCI protection for any circuits in the rooms, smoke/CO detectors, means of egress, etc.