Indeed it should. But, if the device’s battery is very low, the device sometimes doesn’t receive enough juice to run and charge simultaneously.
You are blaming the Enfield’s battery, but in post #10 you found that the same happened when you tried the device on your GSA, too. Is a GSA’s battery / alternator / charging system, known to be crap, too? As it happens on both bikes, that would seem to point to the device, not the bikes.
When the device is on both bikes and the engines running, is there a lightning flash symbol displayed through the battery symbol on the device’s screen, indicating that charging is taking place? Is the lightning symbol displayed all the time that you are riding around, indicating that the device is receiving a permanent live feed?