How does this three wire switch (and LED "ready" indicator) work?

Hello,
I recently bought a fog machine that I want to control via Arduino. Right now it is powered by a three prong extension cord, and then has another, separate three prong power jack. A remote switch plugs into this. Basically it looks like a normal female power plug on one side and then it has the control which is a “ready” led indicator and a push button switch.

I took apart the switch and here is what I found. The “hot” black cord from the power goes to one side of an led. The other side is connected to a 120 k ohm resistor, which is then connected to the green ground cord. (see picture)

My questions are:

  1. How could this led “know” when the fog machine is ready/hot enough to make fog?
  2. If the circuit is not completed until the white wire is attached to the green wire, how can the led be illuminated --or–
  3. If the circuit is completed, why doesn’t it shoot of fog all the time? (In other words, why does the second ground need to be connected to make fog.)
  4. Most importantly, is a relay that connects the white and green cords my only option to trigger this from arduino or is there a way to do this directly from the board (with no external hardware)?

It looks like it just a mains switch inline with the live. there is also a neutral wire so the led can be powered.

With mains voltages a mains-rated relay is one option, but there are others like a mains SSR. Not impressed by that
remote unit (if it is mains) since the connections are bare metal and not protected by sleeving as they should be.

Of course it might not be mains, only seeing how the fog machine is wired inside will confirm that.

I’m sorry-I’m not sure what you mean by “just a mains switch inline with the live”
I tested with a multimeter and it is the black wire (somewhat hidden by the thick black wire) that is positive.
My question relies on this “neutral wire so the led can be powered” If it is ground wouldn’t it cause the fog machine to be constantly running? How can there be a functioning LED circuit if the circuit is only completed when the switch is pressed.

And yes, the remote even feels flimsy-one reason I want to replace it.

Well I said it might not be mains - in which case it will be easier, but first you have
to check the wiring to be sure its not mains (mains has obvious safety implications).
This means looking inside the unit to see what the remote connects to, or finding a
schematic of the unit (sometimes possible for a commercial device, but not often).