I looked through the 360XL manual (downloaded a copy), and there is no mention of the ATS switches. My guess is that it will be near the shore power. On my '94LY the shore power is at the left rear corner, and the ATS switches are located quite high up under the rear panel that swings up behind the radiator (mine is a diesel pusher). At the same time, the main breaker panel for 115volts is located inside the coach, just beside the bed roughly in line with the ATS switches.
Why are you looking for the ATS switches? Is it an issue with a failed component within the ATS switch (I had a burned out time-delay relay in mine which I subsequently sourced, purchased and swapped out the defective one).
1987 Excella 32-foot
1999 Dodge Ram 2500 Diesel