Well. I did some experimenting with the wire element of the controller.
Here the controller is, all dissected. You can see the two pieces of coil that of course, should be one piece.
I figured I would just measure it up, and replicate it. Here you can see, just over 1mm thickness. Look that up on a gauge thickness chart and it you'll see it's 18ga. I also measured the inside diameter of the coils and it was around 7mm. Turned out to be about the diameter of a standard wooden pencil!
Here is the coil I made. At the time I did this, I could only find Galvanized steel wire (or aluminum which wouldn't work), so that's what I used. I did get a piece of 18ga stainless from a buddy that I haven't tried out yet.
And what do you know!!!! It works. I think it has a slight delay on it from my original. I think my original glowed in 11-12 sec and this one is maybe 12-13.