There is a recall on many '04 XB12S bikes that involves replacing the horn mounting bolt with a shorter one. The longer bolt will rub through the horn positive wire and short out when you blow the horn. The engine will shut off when this happens. If your bike is affected, the dealership should perform this repair. Recall info is listed below.
The neutral light coming on when you pull the clutch in is most likely caused by the diode being installed incorrectly or replaced by a fuse. The diode is located in the fuse block. If you're viewing it from the left side of the motorcycle, it should be the second from the rear on the right side. It is part of the starter safety circuit. If it is there, pull it out and turn it around. If it is not there, or in the empty slot, install it correctly. There is a chance it can be another problem, but start here.
Check your build date and see if it qualifies for the recall. Here is the info.
Build Dates : 20030623 - 20030827
NHTSA CAMPAIGN ID Number : 03V494000
Manufacturer Campaign Number: 0828
Component: COMMUNICATIONS:HORN ASSEMBLY
Potential Number Of Units Affected : 581
Summary: ON CERTAIN MOTORCYCLES, THE WIRE THAT PROVIDES POWER TO THE HORN, DUE TO MISROUTING, CAN BECOME FRAYED FROM CONTACT WITH THE HORN BRACKET MOUNTING BOLT. AS A RESULT, THE HORN WIRE MAY BECOME EXPOSED, AND WHEN THE HORN BUTTON IS PUSHED, EITHER THE HORN CIRCUIT FUSE OR THE KEY SWITCH FUSE CAN BLOW.
Consequence: IF THE KEY SWITCH FUSE BLOWS, THE VEHICLE CAN STALL, WHICH COULD RESULT IN A CRASH. IF THE HORN FUSE BLOWS, THERE WILL BE A LOSS OF POWER TO THE HORN AND REAR BRAKE LIGHT.
Remedy: DEALERS WILL INSPECT AND CORRECT THE WIRE ROUTING, IF NECESSARY. OWNER NOTIFICATION BEGAN ON DECEMBER 23, 2003. OWNERS SHOULD CONTACT BUELL AT 1-414-342-4680.