I got my donor reverb tank in, today. Though I've never been inside one of these transducers, fortunately, the internal construction was nearly exactly as I expected - steel loop, with a little round magnet on it, that protruded back through the brass tube and held in place by a big glob of solder. Only the long thin wire was no steel, only the loop. The long thin wire seems to be copper and much finer than I imagined.
One thing I did not count on was that the brass tube was also full of tar. ...or some primitive sort of black silicon glue, but I'm going with tar. This made fishing that super thin wire through the brass tube extremely difficult for even me, a fellow who fishes super fine wire through much smaller holes, daily, in pickups. ...just not
generally full of goop (Bill Lawrence, I'm looking at you!).
Another thing I hadn't counted on was that the brass tubes are held in the black plastic bracket by it being molded around them, apparently. They were not made to come out. ...but with the tar in there, I decided drilling a small hole through the center was the best way to fish the wire clear through the tube and out the other end.
With a little bit of heat, I was able to remove the brass tube, drill through it's tarry center, fish the thin copper wire through and bend and solder it in place.
So, there it is! Fully working (I have another old Twin around to test it with), all period correct parts from Accutronics, and everything original, other than that little steel hook and magnet. Do you suppose the magnets were "better" in 1966 than in 1968? Maybe I've shorted myself!

I laugh at this, but someone will ask me this about a Gibson pickup tomorrow, undoubtedly, and I'll have to give it some honest consideration to provide a fair answer.
I only paid $30 for the donor tank, shipped. It was sold as dead but the only problem was one of the jumper leads to the other transducer had come loose and needed to be soldered back on. So, I've got four more vintage springs, the other whole transducer, half of the transducer I sole my parts from, and the aluminum chassis parts, mounting springs and bumpers, jacks, etc. Nice to have spares or be able to help out a friend in need.
"Unrepairable" part, my ass!