How to fix damaged Gameboy Advance power switch?

So I went to fix the typical “gameboy won’t power on” issue with these by desoldering the metal cover to the internal power switch and cleaning it out with isopropyl alcohol, but when I turned over the internal switch, I noticed that one of the contacts were missing!

I’ve never seen anything quite like this before and figured I could just get a replacement switch online, but I haven’t been able to find any replacement parts! (I’ve actually found just one but it’s quite an unfavorable price).

I was wondering if anyone knew a way to somehow fix the internal switch by adding on some sort of alternative inside contact, or where I can buy a replacement from (heck if anyone happens to have spare parts lying around, let me know).

Also, in regards to buying a replacement, could I buy an internal switch replacement for a different device, like the DS lite? I know the housing pins of the casing for the internal power switch are not the same with the two devices, but I only need the switch inside the housing of the switch, and was wondering if I could just swap out the power switch itself.

Here is a picture for reference - I circled the contact that is missing for me: