game:set_value() is documented here:
https://www.solarus-games.org/doc/1.6/lua_api_game.html#lua_api_game_set_valueIt sets a variable that can be saved in the savegame file, which is what you want if I understand correctly. So that the information (the switch state) is preserved when the player leaves and reenters the map, or even if they save and quit. You just need to choose a name for your saved variable, in my code snippet I put "mymap_interruptor_a" as an example but it is up to you to choose a relevant name. And the value is a boolean: true to indicate that the switch is activated, false (or unset) otherwise.
Then in map:on_started(), call game:get_value() to retrieve the state of the switch, and if it is saved as activated, then activate it with interruptor_a:set_activated(true).
If you are lacking Lua basics in general, I would recommend the Programming in Lua free guide:
https://www.lua.org/pil/contents.htmlPS: I just check tutorial 17. In that tutorial, I use the state of the treasure chest (which is automatically saved, as set by a checkbox in the quest editor) to guess the state of the switch, so actually I don't have to do all that.