Hi Guys-
They make IDC (insulation displacement connectors) that should be able to clamp onto this ribbon cable and allow you to connect other wires into them. You'll need to take a careful measurement of the center to center spacing on the ribbon cable to get the right kind. These are similar to the connectors on the ribbon cables for disk drives in your computer. Allied electronics or AllElectronics are good places to find stuff like this. If you get the flat style, You can usually clamp them onto a ribbon cable using a pair of channel-locks if you're careful.
You might also be able to "split the loom" with a razor knife and get to each wire individually. Then its pretty easy to splice into them.
Hope this helps and thanks for sharing your info.