I did a quick look and it doesn’t look like the switch is directly on the motherboard so most likely there’s a JST plug or something similar with wire leads that then hook into the switch and/or a daughter board. If it’s just two wires into a JST plug you can replace the switch with anything similar or if you wanna be ghetto about it just touch the two wires together to make a short.
You can probably get the exact switch if you look hard enough since almost everything but the exterior shell will be commodity components.
Good luck!
Yikes! That’s just about the worst case scenario. It’s maddening the shortcuts companies play to save literally pennies. Sounds like you’ve at least solved the problem so hopefully the replacement and all that work is fruitful!