The water is getting warm, huh?
I don;t recognize the switch. What I would have done is ordered one for the purpose of playing with it. You might just get that AhHa moment.
Aside:
I just ran into that with a toothbrush. This toothbrush will likely be sacrificial. The battery wasn;t an exact replacement. No polarity markings on the PCB or battery. Just the extended tab. I put a polarity marking on the PCB. If it was an OEM battery, it would have fit one way, I installed it backwards. It briefly make noise. I messed up the charging coil.
Any identifying markings would help.
here
https://www.idec.com/language/english/catalog/Switches/SwitchFamily.pdf#page=18 is an example where it isn't obvious and care is expected.
In many cases the actuator, lighting and contact blocks are separate.
This
is one such similar animal I worked with until Iused about 200+ of them. It was a nice design until "they" redesigned the lens. It was cool because the switches (black section) could be removed, but not purchased
separately, The middle area was reserved for the lamp and the other side contained an optional switch.
They are NO NC switches, not SPDT. it could be wired with 0.110" fastons or solder.
You pushed the yellow writing in on both sides to release the contact block.
The front panel sits between the square metal thing with "dig in tabs". here, the contact block is removed and it's installed from the front. A special tool tightens the castle like nut. It goes together easier that taken apart.
It's very likely, it has to be disconnected/tightened to the panel in the back.