So many posts to catch up on, I'll reply to everyone in the morning!
Just wanted to quickly get
@abracadaver set up before I hit the hay.
First, follow this tutorial:
https://imgur.com/a/nK2vuDx
That will get you most of the way with cleaning the button internals.
You mentioned, "I believe that the wonky function is due to an incomplete contact of the opposing magnet "poles". The magnets shouldn't ever touch. The magnets themselves don't form any part of the circuit. So no worries there.
Your issue does sound like the button isn't making good contact. Even if the bronze surfaces look perfect, I would still give them a clean as per the instruction manual linked above. The "tarnish" of bronze is pretty much invisible.
There could be a little spec of dust or debri in there.
I would also clean the bronze bottom plate around the heater module hole, the heater module shells where they make contact with the bronze, and the screw that goes into the bottom of the button. Might as well clean the connector bridge contacts, but this part is unlikely to be the culprit.
The bronze bottom plate is best cleaned with a pencil eraser as per the tutorial, the heater module shells can be cleaned the same way, or with the grey abrasive pad.
For re-assembly of the button, here is how to put the magnets back into place:
https://imgur.com/a/zQVRoWY
It's a little bit confusing, I know. So please feel free to ask for clarification. I couldn't quite figure out how to photograph it well, maybe I'll have to make a video.
One thing that comes to mind is that maybe your button parts are somehow out of spec, here's something you can check.
Remove the brass button completely, as well as both magnets the black ring, and the black cup.
Clean these parts on some paper towel, clean the inside of the back of the brass button, where the magnet is installed.
Put magnet #1 into the black cup, and put magnet #2 into the black ring. Stick em' all together.
Now insert these four parts into the rear of the brass button. When the magnets and insulators are pushed fully down into the hole, the outside ring of brass (the part that makes electrical contact with the bronze back plate) should be just above the insulator/magnets.
If the insulator/magnet is flush with the contact ring at the back of the brass button, then we have a manufacturing defect that is at fault.
Finally, I have a way for you to test your heater modules to know if they are outputting the correct power. In a dim/dark room, insert a fresh battery around 4.2v and the Low heat module. Remove the glass stem and look down the airway hole directly at the heater coil.
Press the button and count how many seconds go by before the coil
just starts to glow a dull red. The low heater module should reach that point in under 15 seconds. If it doesn't, something is wrong.
Let me know how that goes and we can go from there!
If it's all too much trouble, we can just send it on back here and I'll go over it and test it to make sure it's in tip top shape, certainly sounds like something is amiss with your unit.