The rotten green switch (Pump Motor Switch) is a pressure switch, fabricated mainly from plastic parts. My unit had two, one under the hood and one under an aluminum cover on the chassis (frame rail) just behind the step. the switches are subject to deteriation over time. I bought my first two from a GM parts supplier on line and bought the second two for about a third the cost from Amazon. For my 2004, the following P/N information was correct. I don't know if your year had a different part number:
The GM part number is 15961566. It is stamped on the case. You can order it online at:
Be sure to check price at Amazon.com when you confirm the part number. As a hint, the first sign of failure is when the RGS starts to leak oil.
Do a Google search on Auto Park and you should be able to find lots of information. It has also been discussed on this forum in detail in the past. I would suggest being aware of the system operation, the location of the two switches, and have two spare switches on hand. Failure of the switches will leave you stranded, unless you are prepared.