A friend's ST showed the same signs. It was his battery. It's a good idea to get yours load tested. Having the voltage is one thing. Having the cranking amps is another.
As a battery ages it loses capacity. It gets to the point where riding down the highway keeps the decreasing capacity charged but stop and go traffic draw on the battery as well as the alternator and when you need to start it: surprise.
The friend let his battery charge on a 2A charger (not a tender) for 30min and the ST fired right up. Then we killed the engine and left everything else on (stock bike no farkles) for two minutes. Not even a solenoid click even though the lights were bright. A new battery cured it all. So a load test on your battery would be in order.
I'll add that a 1300 with a
good battery won't last a lot longer! :lol: