Digitech Studio Vocalist

Vocal harmony processor, able to provide real-time harmony to any vocal line.
[product info/review]

Placed on the Pumpkins' official eBay account on 2011/09/29, ending on 2011/10/09 at $200. The accompanying text read:

Digitech Studio Vocalist Vocal Harmony Processor. Used by Billy Corgan. The unit has been kept in a smoke-free studio environment. No cables or manuals are included. A certificate of authenticity will be included. Unit is sold "as is".