Many people hold the start button in for a prolonged period of time and then release it. Yes, the headlight does go out, it's supposed to. That's they way it's designed.
People like me who live in Florida, slather dielectric grease on all connection, bulb sockets and pins. I can hold the switch down for more than 10 seconds and then release it, or as soon as I hear the starter turn, I take my thumb off.
Mine follows this way: Push the start button and the headlight goes off, starter turns over engine; release button, engine starts and headlight comes back on.
When all else fails, read the instructions. This book worth every penny.
Wouldn't run a trike shop without one.