Surely the secondary, once energised, goes to earth via the spark plug gap. My Haynes schematic shows a switching transistor between the LT and HT sides so I would imagine it is that which has failed. The two did not fail simultaneously. I was able to ride a mile or two on one cylinder before it died completely. A couple of times I was able to restart the bike and go about a quarter of a mile before the problem came again.
The weird thing is that although the bike will not now start, the engine management light has gone out and there are no standing faults on the 911.
Just a stab in dark like one says, but how old is your battery, new battery are bigger and more power no packing.
https://www.ukgser.com/forums/showthread.php/559823-1200-GSA-batteries-dead-battery-boost-no-help