That should work fine. You just splice the red wire to the car wire leading to the center terminal, and the black wire to the car wire leading to the outside terminal. I strongly recommend you use solder-shrink splices and not crimp types. To use them:
1) Strip the ends on both wires
2) Slide the shrink onto one of the wires
3) Twist the stripped ends together
4) Slide the solder band inside the shrink over the twisted copper
5) Apply a heat gun or Bic lighter until the solder melts and the plastic shrinks around the wires
Voila, a permanent and waterproof splice. If you use a Bic, keep the shrink in the blue part of the flame and you won't get soot. The shrinks look like the pic below, if you enter "solder shrink" into the eBay or Amazon search bar you'll get a gazillion hits. Some parts stores are also starting to stock them (but of course you'll pay a premium):

- Solder Shrinks.jpg (13.2 KiB) Viewed 1753 times