I would definitely check the light out itself. If you still have your stock tail light, throw it in there and just brake constantly and see what happens. Figure out if its in the wiring or the light itself.
Or you could do the cheap thing, and go by your local shop and pick up a mini 25 fuse and put it in there. Should stop the fuse from blowing.
2005 Ninja ZX6R(636) - Candy Plasma Blue, 8000K HIDs, Solo Seat Cowl,Two Brothers Exhaust, Pirelli Angel ST tires, ProGrips Gel Grips, CA Flushmounts, LP Smoked Integrated Tail Light, Puig Double Bubble Screen, LED Plate Bolt Lights, Speigler Stainless Lines (front)