What is the identity of this shiny insulator?
That is common chromate surface treatment. Seen in a great many metal utility items. Not intended to be an "insulator" but perhaps non-conductive as a side-effect.

The red surface of magnet wire is the enamel insulation which is applied as a coating (vs. being an extruded plastic outer sheath as most other wire uses. They use a very thin enamel insulation to get many windings into the space available in a transformer, coil, solenoid, motor, or whatever.  It is called "enamel" which it probably was in early days. But in modern times, it is a more sophisticated plastic coating of perhaps several layers. Note that red is only perhaps the most popular color. Magnet wire comes in several other insulator colors also.

Ref:  https://en.wikipedia.org/wiki/Chromate_conversion_coating

Ref: https://en.wikipedia.org/wiki/Magnet_wire