Hot days and long rides ? That suggests to me that the tank is getting closer to empty than full when this happen's. The issue: Cut's out and coughing and spluttering, not much engine power. (From Post 1).
When Jo turn's the kill switch off and back on, it works OK for while.
When you turn on the ign switch, you hear the fuel pump pressuring the line to the throttle body injector's. Same happens via the kill switch when the line pressure would be low to nil.
The pump motor runs hotter in prolonged use and a minimum of 1 Litre of fuel is needed after it has reached indicated empty to maintain pump cooling in normal ambient temperatures.
Hot dry air is not normal ambient either.
So on prolonged really hot weather rides, with the fuel low in the tank, the reflected engine heat could be affecting the pump itself or vapourising the fuel in the lines to the injector's (the coughing/spluttering).
If it's got that bad, the ECU (in a GSX-S1000) would be very hot. That sensor 13580 - 14J00 is not from that bike, so what IS the bike were talking about here?
You can never prove vapouring is happening once after the bike got cooler, say in a workshop or the bike has had a chance to cool down a bit.