"defaults": {
	"custom": {
		"groupConfigs": {
			"0": {
				"groups": [ "Ring_Outer", "Gem", "Ring_inner" ],
				"operation": "set_false", // defaults to set_true. Possible values are "set_false", "set_true", "toggle", "none"
				"other": "set_true" // applies to all groups not captured by "groups". defaults to "none".
			}
		}
	}
}

Code (kinda abstract)
createVisibilities() for all groups
for group in groups
	apply "operation"
take the set difference <all groups> - <groups>
apply operation "other"