Reassembling was a bit tricky as the spring needed some pretension (about 1/4 turn or so) to be properly installed. There is probably some special tool the factory used. I got it done by holding the housing in a bench vice and using a thin flathead screwdriver to help with the rotational tensioning.
Obviously to complete the job, re-solder the wires, replace the cap, and reinstall the assembly in the car and reinstall the gas pedal assembly in the car also.
You can also clean and lubricate the cable if desired. I recommend cleaning and lubricating the pedal assembly at this point if you haven't done so already, since it's relatively easy and could help. Enjoy a perfectly smooth accelerator pedal!
Marvel at how much easier the car is to launch from a stop, and how much more of a joy it is to drive!
-END OF DIY-