Look at page 7 of this parts list from our forum library:
https://manuals.heartlandowners.org...rator/Dometic/Dometic NDR1062 3309661.001.pdf
The inset box at the top of the illustration is the switch/light assembly. You will note item 35 only has 1 of these illustrated - actually 4 are used at the corners of the item 27 lamp housing molding. Item 35 is described as an "expansion rivet" . You are probably going to have to clip these plastic rivets off with small wire clippers, and replace them (with maybe something you can find at the hardware store). They might pop loose (reduce expanded diameter) by pushing a small drill bit the size of the inner shaft (you can see the inner shafts of the rivets on a magnified view of your illustration) into them and pulling on the housing.
Item # 41 is the switch, and it might respond to a cleaning with contact cleaner; or you might have a mechanical problem with the actuator parts.
BTW: This is an ammonia adsorbsion refrigerator, and not a residential AC refrigerator. This thread belongs in another section of the Refrigerators part of the appliances forum.
Good luck