I think it is more likely you cut into the harness/circuitry for the kickstand switch or the clutch cut out or the neutral switch. I'd suggest that you carefully go over everything you did electrically to the bike installing your bluetooth. Ideally, you simply grabbed power from the battery or aux. fusebox and did not touch any more of the bike's wiring. Since you said the bike's wiring is a nightmare, it sounds like you made some modifications to it. I would guess that something in your electronics is telling the bike sometimes that the kick stand is down or the clutch is not squeezed while it is in gear.
On my 1300, if the bike is in gear, and the kick stand is down, she will not start. Headlight blinks off as I push the starter button - nothing more. Pull in the clutch, no change. Bike HAS to be in neutral. If the kick stand is up, with the bike in neutral it will start regardless of the clutch position. If kickstand is up, bike in gear, she will start only with clutch pulled in. If the kickstand is down, putting the bike in gear shuts the motor off.
a. What do you mean by clutch in neutral? Clutch pulled in (squeezed)? Clutch released (hands off the clutch lever)?
b. Once you clear up the terminology, we can do a better job of troubleshooting without guessing.
c. What is the transmission position when this unplanned shut down (or no start situation) occurs? In gear or in neutral?