Rickenbacker was really the first company to electrify and market a guitar that could be played on stage and heard over the band. The designs are still relevant today and still copied by many manufacturers.
I have rewound all styles of Rickenbackers. These include the original "Frying Pans" to 4001 basses to the 4002 with a Low Z circuit and all the Rics in between.
Rewinding a Rickenbacker is a challenge due to many factors. The small gauge of wire used, how the coil is wound, and even the assembly on some versions.
The cost is generally $60.00 plus shipping but can fluctuate depending on the model.