I've repaired many rocker switches with various issues. Usually it's the pivot point that holds it together, so using a knife or similar get under the edge of the switch so pry it over the pivot pin. Then one one side is off you should be able to carefully take it off. If not you may have to pry the other side as well. Be careful because they typically have one or two springs inside and you want to put them back in the same spot. Once open take a few good pix of the guts and spring(s) just in case. It may have built up dust/dirt that the grease captured and now it's causing to not make connection, if so, clean it out. If it got too hot then one leg may have moved in the softened plastic and again isn't making connection. You have to push it back and JB Weld or super glue it in place. If it won't move you may have to carefully heat the leg so it softens the plastic, then move it. If the contact points are burnt it may just need sanding to clean it up. If they're so burnt that too much metal is gone then you'll have to push it up to match, like before with force or heating.
It could also be the same contact issues with the external points that it plugs into, or those connectors to the wire. Quite often I find that whatever the problem ends up being, it all started with a poor connection between the external male and female connections. If the contact is poor, like what happens if it's not exactly a tight fit or there's corrosion, it'll get hot there and either start burning the metal until it breaks contact, or melts the plastic and metal parts move until no contact.
If all fails I'd simply connect the wires I want working and call it good. If you actually want to switch then you can pay the $90, or shove a cheap switch in the same spot, or leave it there but move a new switch to elsewhere so everything at least looks oem. Lastly, it's likely possible to glue your rocker cover to a cheap switch and make that cheapie fit in that spot so it both works and looks oem.
Not that it'll help you now, but some switches on some cars I'll use either a transistor or relay to take the abuse. Like those with the headlight switch in the turn sig lever (idiots). So before it fails under all that power I move the headlights to a relay under the dash, then the switch simply operates the coil on the relay which is nothing. Transistors draw even less power but you lose about .6 volts so you don't want them on headlights where that .6 loss will be obvious, but you can have a transistor drive a relay. For example I have one car with a teeny weeny little starter button. Starters already have a relay but this switch would burn up trying to activate it so I have a transistor do that. So with almost no power thru the switch I can start the car. The switch will pretty much last forever too, so whatever kind of switch that is, or is known to be an issue can be fixed like this before it fails. In your case you may find need to use one that's too weak, or if you fix yours it likely won't have the ampacity it once did so. Prolly too much work for this but fyi to keep in mind about misc other stuff.
Oh, and if you need more info or help, just ask. Ideally post pix of it too. Not sure if I'll check back but you can PM me