when I had stopped at light the engines were shut off as expected. where your engines shut off before you moved to neutral?
To avoid confusion, let us call the gas-engine by the term, "ICE" (Internal Combustion Engine).
Your original post describes a situation where the car completely shuts off just because of an accidental shift into NEUTRAL. THis should not happen. The HH should NEVER turn itself OFF unless you physically turn the key to OFF. This is true regardless of what you do with the gear-shift.
The HH will shut off the ICE when it is not needed. This is NOT the same as "turning OFF" the car. The car is still ON and should remain ON with dashboard lit and the "READY" indicator lit unless we turn the key to shut everything down.
The ICE activates and deactivates depending on when it is needed. Sometimes, if the battery needs charging, the ICE will run as long as needed to charge the battery even if the car is sitting idle. Sometimes, if the battery is full and the car is moving at very low speed, the ICE remains OFF while the car runs completely on electrical power only. Sometimes, the car runs on both ICE and electrical power especially when towing, accelerating or climbing. In all these events, the car is ON and must remain ON regardless of whether the ICE is running. The only time the car should be OFF is if you physically turn the key to OFF.
So, unless I am misreading your post, the sudden complete shutdown of the car at a traffic light is abnormal if you did not turn off the car.
As for shifting to NEUTRAL, it does not turn OFF the car. I shift to NEUTRAL when the battery is full and I want to glide without any regeneration to slow the car. It is something I do on certain flat roads around our house. The car remains ON and ready to roll when I shift back to "D".
The HH is really no different than a normal car in terms of when it should be ON or OFF. As long as the key is in the ON position, the HH must remain ON. WHen the key is in the OFF position, then the car is OFF.