Help Finding An AF Part or Encouragement

You are correct, the ideal solution is for someone on the forum to have a spare... but unfortunately, I'm not that guy!  Hopefully, someone will have an extra for you.

I don't fear winding a coil, and it sounds like you are game for it, too.  Personally, I prefer to use new wire to rewind.  The old wire is probably more brittle than new wire, and the process of unwinding and rewinding it could work harden it even more, making it even more likely to break.  Just make sure to count the turns when you unwind the coil.

However, the only downside to trying to reuse the old wire is lost time.  It will take more time to unwind, keeping the old wire in useable condition, perhaps by rolling it on a spool.  If you use the old wire and it fails again in the near future, you can unwind it again and rewind it with new wire at that point.  It's up to you if you want to spend the money on new wire now, or spend the time to use the old wire with a greater chance of breaking the wire during the rewinding or having a failure later on.  I suspect that if you get it rewound with the old wire and it works, it probably won't give you any problems in the foreseeable future.

I can still remember my first experience with winding coils... holding a spool of magnet wire, keeping the correct tension while my Dad wound a low tension coil for an igniter on a hit-and-miss farm engine!  It's interesting what experiences will make an impression on a young kid.

 It looks like a re-wind for sure. Just unwind the old wire and measure the length. New magnetic wire is fairly inexpensive and is worth the effort. It is now difficult to do, just keep constant tension when winding and keep the windings tight to each other. If you are within a foot or so left over, consider it a success!

  I would not use the old wiring for anything as the insulation has usually broken down and you may get shorts in the windings. Just MHO. Al

It might be worth drilling the rivet, if you can find a suitable replacement, and seeing if you can get to the end of the wire.  If you can already tell it's no go, then, rewind it.  Been there done that, just takes some patience ( which I am usually short on) but it's not a big deal.  Just make sure you do your best to keep the wraps neat and tidy, otherwise it will produce a "fatter" coil for the same turns and it might not fit where it used to!  good luck, but it ain't hard

I've rewound coils from time to time. IMHO, if you can get some new magnet wire, on a small spool, the job will go alot better.