Wikipedia and other sources state that the Independence carried 7 guns. six 6-pound guns in broadside and one 9-pound gun mounted in a pivot. This allowed the Independence to fire three 6-pound guns and one 9-pound gun to port or starboard.

Does anyone know where the pivot gun was mounted?

The Independence began it's life as the US Revenue Cutter Samuel D. Ingham (http://en.wikipedia.org/wiki/USRC_Ingham_%281832%29). Looking at H.I. Chapelle's drawing of the Indenpence's sister ship the Revenue Cutter Roger B. Taney,there does not appear to be enough room to mount the pivot on the forecastle (before the foremast) because of the windlass and the kingposts. The drawings also show that a capstan was mounted midship, between the foremast and mainmast. If there was no capstan than the midship area would have been the perfect location for the pivot gun.