12-string acoustic guitar, used on Adore. Was also used in the Chicago Songs recording sessions at The Temple (Dmitre Photography) in April 2004.
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Listed on the Pumpkins' official eBay account on 2012/10/16, ending on 2012/10/23 at $3500. Auction text was as follows:

Here is 12 string acoustic Guild guitar that was used by Billy Corgan on the Adore album.
Serial # JF6512BI
Model # AJ620155
Guitar case is included in this auction.
This guitar is sold used as is.
This guitar will come with a certificate of authenticity issued from Smashing Pumpkins memorabilia.

Note the actual model number is JF65-12, and AJ620155 is the serial number, indicating that it was made in 1995. A sticker on the back of the headstock indicates that it was likely kept in C tuning.